Suppose that the functions f and g and their derivatives with respect to x have the following values at the given values of
x. Find the derivative with respect to x of the given combination at the given value of x.
-

$1 / g ^ { 2 } ( x ) , x = 4$
A) $- \frac { 2 } { 27 }$
B) $\frac { 2 } { 125 }$
C) $- \frac { 10 } { 27 }$
D) $\frac { 10 } { 27 }$

Question

Suppose that the functions f and g and their derivatives with respect to x have the following values at the given values of
x. Find the derivative with respect to x of the given combination at the given value of x.
-

$1 / g ^ { 2 } ( x ) , x = 4$
A) $- \frac { 2 } { 27 }$ 
B) $\frac { 2 } { 125 }$ 
C) $- \frac { 10 } { 27 }$ 
D) $\frac { 10 } { 27 }$

Quizplus · Accepted Answer

Using the chain rule, we have:

$$\frac{d}{dx}\left(\frac{1}{g^2(x)}\right)=-\frac{2g'(x)}{g^3(x)}$$

Plugging in x = 4 and using the values given in the table, we get:

$$\frac{d}{dx}\left(\frac{1}{g^2(x)}\right)\Bigg|_{x=4}=-\frac{2g'(4)}{g^3(4)}=-\frac{2\cdot (-5)}{(-2)^3}=\frac{10}{27}$$

Therefore, the answer is D.

Suppose That the Functions F and G and Their Derivatives 1/g2(x),x=41 / g ^ { 2 } ( x ) , x = 41/g2(x),x=4

Suppose That the Functions F and G and Their Derivatives $1 / g ^ { 2 } ( x ) , x = 4$