The chain rule is a fundamental concept in calculus that allows us to differentiate composite functions, which are functions that are formed by combining two or more simpler functions.
The chain rule states that the derivative of a composite function is equal to the derivative of the outer function evaluated at the inner function, multiplied by the derivative of the inner function with respect to its argument.
In your question,
We have two functions: h(u) and u(x).
The function h(u) depends on the variable u, while u(x) depends on the variable x.
To differentiate h(u) with respect to x, we need to use the chain rule. We can write the chain rule as follows:
dh/dx = dh/du * du/dx
Here, dh/du represents the derivative of the function h(u) with respect to u, while du/dx represents the derivative of the function u(x) with respect to x.
The chain rule tells us that to find the derivative of the composite function h(u(x)), we need to multiply the derivative of the outer function h(u) with respect to its argument u (i.e., dh/du) by the derivative of the inner function u(x) with respect to its argument x (i.e., du/dx).
In other words,
The chain rule allows us to "chain" together the derivatives of the two functions to find the derivative of the composite function.
By applying the chain rule, we can calculate the derivative dh/dx in terms of the derivatives dh/du and du/dx.
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When we apply the chain rule for functions h(u) and u(x), we can express the rate of change of h with respect to x in terms of the rates of change of h with respect to u and u with respect to x. Using the chain rule formula, we have: dh/dx = (dh/du) * (du/dx)
This means that the rate of change of h with respect to x is equal to the product of the rate of change of h with respect to u and the rate of change of u with respect to x. This formula is useful in calculating derivatives in cases where a function is composed of multiple functions nested within each other.
The correct formula should be:
dh/dx = dh/du * du/dx
Now, to answer your question using the chain rule for functions h(u) and u(x), we can follow these steps:
1. Find the derivative of h(u) with respect to u, which is dh/du.
2. Find the derivative of u(x) with respect to x, which is du/dx.
3. Multiply the results of steps 1 and 2 to obtain the derivative of h(u(x)) with respect to x, which is dh/dx.
So, by applying the chain rule to functions h(u) and u(x), we have:
dh/dx = dh/du * du/dx
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Can someone help me with this
I’ll mark as brainliest.
Answer:
The W/C is divided by the numbers on top to the number on the bottom
may i have brainlist??
PLZ help me i need the answer asap 7th grade math
Answer:
43.98
Step-by-step explanation:
2(pi)(7)=43.98
2(pi)(r)
what is 40% of 10? PLZ HELP ASAP
Answer:
4
Step-by-step explanation:
10 * 40%
10 * 0.4 = 4
Answer:
Hi! 40% of 10=4
Step-by-step explanation:
Hope this helps! :)
Have a nice day! ♥
what is 64 ÷8 x 1/2 Please and Thank you
Answer:
4
Step-by-step explanation:
64/8 x 0.5 = 8 x 0.5 = 4
What is the slope of the line that passes through these two points (15,20) and (20,25)
Answer:
The slope Is 1.
Step-by-step explanation:
If you graph the two points it shows that the graph is done.
Answer:
slope = 1
Step-by-step explanation:
Calculate the slope m using the slope formula
m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]
with (x₁, y₁ ) = (15, 20) and (x₂, y₂ ) = (20, 25)
m = [tex]\frac{25-20}{20-15}[/tex] = [tex]\frac{5}{5}[/tex] = 1
The six sided of number cube are labeled 1,2,3,4,5 and 6. You flip a coin and roll the number cube. What is the theoretical probability that the coin lands on heads and roll a number greater than 2?
heads = 1/2
>2 = 2/3
2/3 x 1/2 = 1/3
Answer:
1 / 3ANSWER ASAP GIVING BRAINLIEST FIVE STARS AND A HEART I ONLY NEED A FEW SENTENCES!
Please answer the following essay question:
An isosceles triangle has two congruent angles. Write an expression to represent the measure of the third angle of the triangle. Explain.
Step-by-step explanation:
Let x be the size of 1 of the 2 congruent angles.
The size of the other congruent angle is also x.
Since sum of angles in a triangle = 180°,
Measure of 3rd angle in the triangle
= 180° - 1st angle - 2nd angle
= (180 - 2x)°.
Answer:
The Isosceles Triangle Theorem, All interior angles of a triangle add up to 180 degrees. Basically the equation would be (angle 1) + (angle 2) + (angle 3) = 180. whichever angle you dont have you replace with x and solve for it. For example if you had a triangle with two congruent angles of 36 then it would be 36+36+x=180 and you would solve it like any other equation eventually showing you that x = 108. it also works backwards if you are trying to solve for the 2 missing congruent angles.
Step-by-step explanation:
A square cake sits on a circular cake stand. The circular cake stand has a diameter of 24 inches. The cake measures 16 inches on each side. How many square inches of the cake stand are visible?
Answer:
196.12 in^2
Step-by-step explanation:
circular cake stand area=(24/2)^2(3.14)=452.12 in^2
square cake=16x16=256 in^2
452.12-256=196.12 in^2
find the value of 3 under root 54/250
Answer:
Evaluate cube root of 250- cube root of 54
3√250−3√54
Simplify each term.
53√2−33√2
Subtract 33√2 from 53√2-
2^3√2
The result can be shown in multiple forms.
Exact Form:
23√2
Decimal Form:
2.51984209....
Step-by-step explanation:
Hope it is helpful.....
The value of 3 under root 54/250 is 3 / 5.
What is a fraction?A fraction is a numeral that represents a rational number.
Let a and b be two numbers, then their fraction can be represented as a/b.
The given fraction is,
54 / 250.
To find the value of 3 under root 54 /250,
Find cube root of 54 /250.
∛(54 / 250)
= ∛(27 / 125)
= ∛27 / ∛125
= 3 / 5
The value of cube root of 54 /250 is 3/5.
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Once again, I’m wasting points to dazzle you all with my hand drawn cardboard cutouts of hanako and tsukasa. If you don’t know who they are then just admire the art and pretend I’m picasso. Bring up the mistakes and I’ll laugh along and criticize my art with you
Answer:
Cool art
Step-by-step explanation:
Answer:
sick bro, that's cool.
Step-by-step explanation:
do you read the manga, if you do then, broo the lastest chapter was
nice
A recipe needs 1/4 tablespoons salt. the same recipe is made 5 times how much salt is used?
BTW IM IN 8TH GRADE BUT THE SCHOOL HAS NUN 4 US TO DO SO NOW THERE MAKING US LEARN THE SAME STUFF AGAIN AND I DONT REMEBER SO YA
Answer: 1 and one fourths because 1/4 times 5 is 1 1/4
Step-by-step explanation:
Answer:
1 1/4 tablespoons
Step-by-step explanation:
1/4 x 5=1 1/4 tablespoons
there is a line whose y-intercept is 10 and whose slope is -1/2. what is its equation in slope-intercept form? y= x +
Coty painted a right triangle on paper. The hypotenuse of his triangle is 18 inches and one of the legs is 7 inches. What is the length of third side?
Answer:
G) 16.6
Step-by-step explanation:
We can use the pythagoriam theroem to solve the problem
[tex]a^{2} + b^{2} = c^{2}[/tex]
[tex]a^{2} + 7^{2} = 18^{2}[/tex]
[tex]a^{2}[/tex] + 49 = 324
[tex]a^{2}[/tex] = 275
a = 16.6
What is the value of x2 + 3.4y when x = 4 and y = 2?
Answer:
14.8
Step-by-step explanation:
4(2)+3.4(2)
8+6.8
14.8
When someone throws a ball, the action force is the person pushing on the ball. What is the reaction force?
Give a real answer and explain.
Answer:
Should be : The Ball Pushing On The Person
Step-by-step explanation:
while the Air resistance answers have a point this question is asking about the reaction and the only reaction answer is the ball pushing on the person. every action has a reaction,
The ball wants to stay still so it pushes back on the person with all it's force, but the person pushes the ball with more force then the ball has so the ball rolls.
(may have explained it to much or weirdly sorry)
Can someone solve this for me?
2x + 7y = 4
( u have to put it in y = mx + b)
* but when i divide i get y = -2/7x + 4/7
is the 4/7 correct?
like r u allowed to have two fractions?
Answer:
I think that is correct because I got the same answer
Solve the inequality.
Step-by-step explanation:
subtract the value by placing it in the right side and multiply with 4.
To choose the 8 songs, the director writes the name of each of the 12 songs on a slip of paper, puts them in a hat, and draws 8 slips. What is the probability that the set s/he chooses contains two of the four songs that have soprano solos?
Answer:
0.339
Step-by-step explanation:
Given that :
Total number of songs = 12
Number of songs to choose = 8
Total number of draws = 8
Selecting 2 of the 4 songs with syprano solos : 4C2
The 6 remaining songs from. The rest:
12-4C8-2 = 8C6
Total possible selections = 12C8
Hence,
probability that the set s/he chooses contains two of the four songs that have soprano solos will be :
(4C2 * 8C6) / 12C8
(6 * 28) / 495
168 / 495
= 0.339
pls help asap i will give branilest
15.010495
The caluclator can comfirm
Is 299 in the sequence of 2 5 8 11 14 with 3n-1 as the term
Answer:
yes
Step-by-step explanation:
Equate
3n - 1 = 299 ( add 1 to both sides )
3n = 300 ( divide both sides by 3 )
n = 100
Then 299 is the 100 th term of the sequence
y=3x+−7
Find the slope.
A. 7
B. -7
C. 3x
D. 3
Answer:
D.3
Step-by-step explanation:
In the equation for a line in the form y=mx+c, m represents the slope.
Therefore the slope is 3.
Answer:
D
Step-by-step explanation:
The equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
y = 3x + - 7 ← is in slope- intercept form
with slope m = 3
What is a equivalent expression to this expression?c(4a+b)
Answer:
The answer is 4ac+bc u have to multiply
Find the missing angle measurement in the triangle.
Answer:
the answer is C
Step-by-step explanation:
the right angle is = 90
the other angle= 55
so you add them together which makes 145
so subtract 180 which is = to a triangle subtract 180-145=35
Answer: C.)
Step-by-step explanation:
Triangle angles add up to 180 degrees.
The box is a right angle which equals 90 degrees.
55 degrees + 90 degrees = 145 degrees, but we need the sum to be 180, so we subtract 145 from 180 and you should get the answer of "35".
Do the following lengths form a right triangle?
Answer:
2 3 4 do, 1 does not
Step-by-step explanation:
Using the Pythagorean Theorem, we can see that the square of the 2 smaller sides, when added together, is equal to the square of the longer side of each of the example triangles.
The track team sold 40 t-shirts. Short sleeve t-shirts sold for $9.90 and long sleeve
t-shirts sold for $12.75. In all, $421.65 was taken in.
How many short sleeve t-shirts were sold?
Answer:
The track team sold 31 short sleeved t-shirts.
Step-by-step explanation:
If there were 40 t-shirts sold, then you'd have to find how many short sleeved and long sleeved t-shirts were sold to get the amount of money made. Basically, all I did was start with 20:20. I multiplied the cost of each type of shirt by 20, however, the money from selling long sleeved t-shirts is a lot more than the actually amount. So then, I went to 30:10 with short sleeved and then long sleeved. The amount (when added together) was pretty close to the actual amount but it was still a tiny bit higher than the actual. So, I did 31:9 and the amount came out right.
Which properties justify the steps taken to solve the system? {2a+7b=03a−5b=31 10a+35b=0; 21a−35b=217 31a = 217 a = 7 2(7)+7b=0 14 + 7b = 0 7b=−14 b=−2 what are each of the steps taken?
9514 1404 393
Explanation:
2a+7b=0 . . . . . . . . given [eq1]
3a−5b=31 . . . . . . . .given [eq2]
10a+35b=0 . . . . . . multiplication property of equality 5×[eq1] = [eq3]
21a−35b=217 . . . . .multiplication property of equality 7×[eq2] = [eq4]
31a = 217 . . . . . . . . addition/substitution properties of equality [eq3]+[eq4]
a = 7 . . . . . . . . . . . . division property of equality (÷31)
2(7)+7b=0 . . . . . . . .substitution property of equality; a=7 in [eq1]
14 + 7b = 0 . . . . . . . properties of real numbers
7b=−14 . . . . . . . . . . addition property of equality; add -14
b=−2 . . . . . . . . . . . . division property of equality (÷7)
Plzzzzz help!
What is the perimeter of the composite figure?
Answer:
107.5 cm
Step-by-step explanation:
find the length of the missing side of triangle which is 22.5 rounded then add all the sides together
Which of the following shows the greatest percent increase?
A. 50 increased to 75
B. 500 increased to 700
C. 5,000 increased to 7,000
D. 50,000 increased to 74,000
can you please help me
Answer:
b !! (0.5, 0.5)
Step-by-step explanation:
if you used the formula to find midpoint 9i included a picture, you would get the fractions (1/2, 1/2) !! that as a decimal is 0.5 !! so the answer is b !! i really hope this helps !!
A rectangular playground is 65m long and 30 m wide. A pathway of 1.5 m width goes all around, outside it. Find the area of the pathway
Answer:
97.5 m^2
Step-by-step explanation:
Given data
Length = 65m
Width= 30m
We are told that the width of the path= 1.5m
Hence the area of the path is
=65*1.5
=97.5 m^2