what is the value of d/dx(1/x) at x=6 ?​

If you know your derivative rules, then

d/dx [1/x] = -1/x ²

so that when x = 6, the derivative has a value of -1/36.

If you have to use the definition of the derivative, then

d/dx [1/x] = lim {h → 0} (1/(x + h) - 1/x) / h

… = lim {h → 0} (x - (x + h)) / (hx (x + h))

… = lim {h → 0} (-h) / (hx (x + h))

… = lim {h → 0} (-1) / (x (x + h))

… = -1/x ²

and at x = 6, you again get -1/36.

Alternatively, use the definition of the derivative at a point:

d/dx [1/x] (6) = lim {x → 6} (1/x - 1/6) / (x - 6)

… = lim {x → 6} ((6 - x) / (6x)) / (x - 6)

… = lim {x → 6} -(x - 6) / (6x (x - 6))

… = lim {x → 6} (-1) / (6x)

… = -1/36

A student who is trying to write a paper for a course has a choice of two topics, A and B. If topic A is chosen, the student will order two books through interlibrary loan, whereas if topic B is chosen, the student will order four books. The student believes that a good paper necessitates receiving and using at least half the books ordered for either topic chosen. If the probability that a book ordered through interlibrary loan actually arrives in time is .9 and books arrive independently of one another, which topic should the student choose to maximize the probability of writing a good paper? What if the arrival probability is only .5 instead of .9?

Tthere are 5 people already in the pool.jonas and his 2 friends get in.how many people are in the pool ​

If y varies directly as x
and x= 4 when y = 14,
find y when x = -10.

which fraction is equevleint to 5/7

i dont know this help me

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the entrance fee for daily tasks zoo is $8.50 per person the price for a monthly passes $52.50 if Maya goes to the zoo 10 times this month how much would she save by purchasing a monthly pass​

Given h(x) = 4x2 - 5x + 4 find h(-5).

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directions: solve each equation below and type your answer in the answer column. Type all answers in decimal form

$3.50 nail polish marked up to $8.75. explain it please like example. ​

I need help ? Answer below

the ratio of the number of girls to the number of boys in a school is 9:10. There are 900 boys in the school.
Work out the total number of students in the school

at Kayla swimwear 6 out of 20 style at the store are bikinis what percentage of swimsuit styles at the store are bikinis​

What is 80% as a fraction in reduced form? StartFraction 1 Over 8 EndFraction StartFraction 4 Over 5 EndFraction StartFraction 8 Over 10 EndFraction StartFraction 40 Over 50 EndFraction

Using the textbook example of 420 California school districts and the regression of testscores on the student-teacher ratio, you find that the standard error on the slope coefficient is 0.51 when using the heteroskedasticity robust formula, while it is 0.48 when employing the homoskedasticity only formula. When calculating the t-statistic, the recommended procedure is to A. use the homoskedasticity only formula because the t-statistic becomes larger B. first test for homoskedasticity of the errors and then make a decision C. use the heteroskedasticity robust formula D. make a decision depending on how much different the estimate of the slope is under the two procedures

Can some plz help me I need it rn

Identify the reason that justifies each statement.

One lap around the lake is 710 mile.
Dasha runs 9 laps around the lake.

Use the drop-down menus to complete the equation.

2x+9y=8 and 2x-9y=8 as an ordered pair

Reflect the trapezoid in the x-axis. Then translate the trapezoid 2 units left and 3 units up. The coordinates of the final image are:

-3xy-x²y²+1 is evaluated when x=-1 and y=-1 , then what is the exact value ?
​

I will mark genius!!! Please help
change the fraction to a decimal and a percent. go three decimal places

line p had a slope of 5/4. line q is perpendicular to line p. what is the slope of line q?

Name the quadrant in which lies.
tan(theta)<0 , csc(theta)<0
The angle (theta) lies in which​ quadrant?

four pieces of pie were eaten from a pie cut into equal parts. The 5 pieces that remained created an angle that measured 200°. What was the angle measure of one piece of pie

Make y the subject of the following equation.
5x + y = -10
a. y = -5x + 10
b. y=-10 - 5x
c. y = -10 + 5x
d. y + 10 = -5x​

Solve the equation. Please make sure you double-check your solution (answer).
15 = z -35

166. Запишите все целые числа, расположенные на координатной прямой между числами:

Use SSS, SAS, ASA, AAS, or Not Enough Information to identify the postulate or theorem that immediately confirms the congruence for each pair of triangles. Justify your answer.