Find the derivative of $f ( x ) = \sqrt { 9 x }$ .
A) $\frac { 3 } { 2 \sqrt { x } }$

B) $- \frac { 3 } { 2 \sqrt { x } }$
C) $\frac { 9 } { 2 \sqrt { x } }$
D) $- \frac { 9 } { 2 \sqrt { x } }$
E) $\frac { 3 } { \sqrt { x } }$
F) $- 3 \sqrt { x }$

G) $3 \sqrt { x }$

H)None of the above

Question

Find the derivative of $f ( x ) = \sqrt { 9 x }$ .
A) $\frac { 3 } { 2 \sqrt { x } }$

B) $- \frac { 3 } { 2 \sqrt { x } }$
C) $\frac { 9 } { 2 \sqrt { x } }$
D) $- \frac { 9 } { 2 \sqrt { x } }$
E) $\frac { 3 } { \sqrt { x } }$
F) $- 3 \sqrt { x }$

G) $3 \sqrt { x }$

H)None of the above

Quizplus · Accepted Answer

The derivative of $f(x) = \sqrt{9x}$ can be found by first expressing the function as $f(x) = (9x)^{1/2}$ and then applying the chain rule. The derivative is $f'(x) = \frac{1}{2}(9x)^{-1/2} \cdot 9 = \frac{9}{2\sqrt{9x}}$, which simplifies to $\frac{3}{2\sqrt{x}}$, matching option A.

Find the Derivative Of f(x)=9xf ( x ) = \sqrt { 9 x }f(x)=9x​

Find the Derivative Of $f ( x ) = \sqrt { 9 x }$