$\text { Find the derivative of the function } f ( x ) = 9 \sqrt { x } \sin ( x ) \text {. }$
A) $\frac { 9 } { 2 } \sqrt { x } \sin ( x ) + 9 \sqrt { x } \cos ( x )$
B) $\frac { 9 } { 2 \sqrt { x } } \sin ( x ) + 9 \sqrt { x } \cos ( x )$
C) $\frac { 9 } { 2 \sqrt { x } } \cos ( x )$
D) $\frac { - 9 } { 2 \sqrt { x } } \sin ( x ) + 9 \sqrt { x } \cos ( x )$
E) $\frac { 9 } { 2 \sqrt { x } } \sin ( x ) - 9 \sqrt { x } \cos ( x )$

Question

$\text { Find the derivative of the function } f ( x ) = 9 \sqrt { x } \sin ( x ) \text {. }$ 
A) $\frac { 9 } { 2 } \sqrt { x } \sin ( x ) + 9 \sqrt { x } \cos ( x )$
B) $\frac { 9 } { 2 \sqrt { x } } \sin ( x ) + 9 \sqrt { x } \cos ( x )$
C) $\frac { 9 } { 2 \sqrt { x } } \cos ( x )$
D) $\frac { - 9 } { 2 \sqrt { x } } \sin ( x ) + 9 \sqrt { x } \cos ( x )$
E) $\frac { 9 } { 2 \sqrt { x } } \sin ( x ) - 9 \sqrt { x } \cos ( x )$

Quizplus · Accepted Answer

To find the derivative of $f(x) = 9\sqrt{x}\sin(x)$, we use the product rule and the chain rule. The derivative of $9\sqrt{x}$ is $\frac{9}{2\sqrt{x}}$, and the derivative of $\sin(x)$ is $\cos(x)$. Applying the product rule, we get $\frac{9}{2\sqrt{x}}\sin(x) + 9\sqrt{x}\cos(x)$.

Find the derivative of the function f(x)=9xsin⁡(x). \text { Find the derivative of the function } f ( x ) = 9 \sqrt { x } \sin ( x ) \text {. } Find the derivative of the function f(x)=9x​sin(x).

$\text { Find the derivative of the function } f ( x ) = 9 \sqrt { x } \sin ( x ) \text {. }$