Find the derivative of the function. $f ( x ) = \frac { 1 } { \sqrt { x - 4 } }$
A) $\frac { 1 } { 2 ( x - 4 ) ^ { \frac { 3 } { 2 } } }$
B) $\frac { 1 } { 2 ( x + 4 ) ^ { \frac { 3 } { 2 } } }$
C) $\frac { 1 } { ( x + 4 ) ^ { 2 } }$
D) $\frac { 1 } { 2 \sqrt { x - 4 } }$
E) $- \frac { 1 } { 2 ( x - 4 ) ^ { \frac { 3 } { 2 } } }$

Question

Find the derivative of the function.   $f ( x ) = \frac { 1 } { \sqrt { x - 4 } }$  
A) $\frac { 1 } { 2 ( x - 4 ) ^ { \frac { 3 } { 2 } } }$
B) $\frac { 1 } { 2 ( x + 4 ) ^ { \frac { 3 } { 2 } } }$
C) $\frac { 1 } { ( x + 4 ) ^ { 2 } }$
D) $\frac { 1 } { 2 \sqrt { x - 4 } }$
E) $- \frac { 1 } { 2 ( x - 4 ) ^ { \frac { 3 } { 2 } } }$

Quizplus · Accepted Answer

The derivative of $f(x) = \frac{1}{\sqrt{x - 4}}$ can be found using the chain rule. First, rewrite the function as $f(x) = (x - 4)^{-\frac{1}{2}}$. Applying the chain rule, the derivative is $f'(x) = -\frac{1}{2}(x - 4)^{-\frac{3}{2}} \cdot 1$, which simplifies to $-\frac{1}{2}(x - 4)^{-\frac{3}{2}}$, matching choice E.

Find the Derivative of the Function f(x)=1x−4f ( x ) = \frac { 1 } { \sqrt { x - 4 } }f(x)=x−4​1​

Find the Derivative of the Function $f ( x ) = \frac { 1 } { \sqrt { x - 4 } }$