Find the derivative of $f ( x ) = \sin ^ { 3 } x$ .
A) $3 \cos ^ { 2 } x$
B) $\cos \left( 3 x ^ { 2 } \right)$
C) $3 \sin ^ { 2 } x$
D) $3 \sin ^ { 2 } x \cos x$
E) $3 x ^ { 2 } \sin x$
F) $3 x ^ { 2 } \cos \left( x ^ { 3 } \right)$
G) $3 x ^ { 2 } \cos x$
H)None of these

Question

Find the derivative of $f ( x ) = \sin ^ { 3 } x$ .
A) $3 \cos ^ { 2 } x$ 
B) $\cos \left( 3 x ^ { 2 } \right)$
C) $3 \sin ^ { 2 } x$
D) $3 \sin ^ { 2 } x \cos x$
E) $3 x ^ { 2 } \sin x$ 
F) $3 x ^ { 2 } \cos \left( x ^ { 3 } \right)$
G) $3 x ^ { 2 } \cos x$
H)None of these

Quizplus · Accepted Answer

To find the derivative of $f(x) = \sin^3 x$, we use the chain rule. The outer function is $u^3$ with $u = \sin x$, and its derivative is $3u^2$. The inner function is $\sin x$, whose derivative is $\cos x$. Applying the chain rule, we get $3(\sin^2 x)(\cos x)$.

Find the Derivative Of f(x)=sin⁡3xf ( x ) = \sin ^ { 3 } xf(x)=sin3x

Find the Derivative Of $f ( x ) = \sin ^ { 3 } x$