Differentiate the function.
$$y = \ln \left( x ^ { 3 } \sin ^ { 2 } x \right)$$
A)
$y ^ { \prime } = \frac { 3 \cos x + 2 x \sin x } { x \cos x }$
B)
$y ^ { \prime } = \frac { 3 x ^ { 2 } + \cos x \sin x } { \cos x }$
C)
$y ^ { \prime } = \frac { 3 \sin x + x \cos x } { x ^ { 3 } \sin ^ { 2 } x }$
D)
$y ^ { \prime } = \frac { 3 \sin x - 2 x } { x \sin x }$
E)
$y ^ { t } = \frac { 3 \sin x + 2 x \cos x } { x \sin x }$

Question

Quizplus · Accepted Answer

The derivative of $y = \ln(x^3 \sin^2 x)$ is found using the chain rule and properties of logarithms: $y' = \frac{3}{x} + \frac{2 \cos x}{\sin x} = \frac{3 \sin x + 2 x \cos x}{x \sin x}$.

Differentiate the Function y=ln⁡(x3sin⁡2x)y = \ln \left( x ^ { 3 } \sin ^ { 2 } x \right)y=ln(x3sin2x)

Differentiate the Function $y = \ln \left( x ^ { 3 } \sin ^ { 2 } x \right)$