Find the derivative of $f ( x ) = \sin ^ { 2 } x$ .
A)2cos x
B)cos( $x ^ { 2 }$ )
C)2sin x
D) $\cos ^ { 2 } x$
E) $2 \cos ^ { 2 } x$
F) $2 \cos \left( x ^ { 2 } \right)$
G) $2 \sin x \cos x$
H) $- 2 \sin x \cos x$

Question

Find the derivative of $f ( x ) = \sin ^ { 2 } x$ .
A)2cos x
B)cos( $x ^ { 2 }$ )
C)2sin x
D) $\cos ^ { 2 } x$ 
E) $2 \cos ^ { 2 } x$ 
F) $2 \cos \left( x ^ { 2 } \right)$
G) $2 \sin x \cos x$
H) $- 2 \sin x \cos x$

Quizplus · Accepted Answer

To find the derivative of $f(x) = \sin^2x$, we use the chain rule. The outer function is $g(u) = u^2$ with $u = \sin(x)$, and the inner function is $h(x) = \sin(x)$. The derivative of $g(u)$ with respect to $u$ is $2u$, and the derivative of $h(x)$ with respect to $x$ is $\cos(x)$. Applying the chain rule, we get $f'(x) = 2\sin(x)\cos(x)$.

Find the Derivative Of f(x)=sin⁡2xf ( x ) = \sin ^ { 2 } xf(x)=sin2x

Find the Derivative Of $f ( x ) = \sin ^ { 2 } x$