Find dy.
-$$y = \cos ( 3 \sqrt { x } )$$
A) $\left( \frac { 3 \sin ( 3 \sqrt { x } ) } { 2 \sqrt { x } } \right) d x$
B) $\left( \frac { - 3 \sqrt { x } \sin ( 3 \sqrt { x } ) } { 2 } \right) d x$
C) $\left( \frac { 3 \sqrt { x } \sin ( 3 \sqrt { x } ) } { 2 } \right) d x$
D) $\left( \frac { - 3 \sin ( 3 \sqrt { x } ) } { 2 \sqrt { x } } \right) d x$

Question

Quizplus · Accepted Answer

To find $dy$, we differentiate $y = \cos(3\sqrt{x})$ with respect to $x$. Using the chain rule, the derivative of $\cos(3\sqrt{x})$ is $-\sin(3\sqrt{x})$ times the derivative of $3\sqrt{x}$, which is $\frac{3}{2\sqrt{x}}$. Therefore, $dy = \left( \frac{-3\sin(3\sqrt{x})}{2\sqrt{x}} \right) dx$.

Find Dy - y=cos⁡(3x)y = \cos ( 3 \sqrt { x } )y=cos(3x​)

Find Dy
- $y = \cos ( 3 \sqrt { x } )$