Find the derivative of $f ( x ) = \sin \left( x ^ { 3 } \right)$ .
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 $f ( x ) = \sin \left( x ^ { 3 } \right)$ .
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 $f(x) = \sin(x^3)$, we use the chain rule. The outer function is $\sin(u)$ with $u = x^3$. The derivative of $\sin(u)$ with respect to $u$ is $\cos(u)$, and the derivative of $u = x^3$ with respect to $x$ is $3x^2$. Applying the chain rule, we get $f'(x) = \cos(x^3) \cdot 3x^2$, which matches option F.

Find the Derivative Of f(x)=sin⁡(x3)f ( x ) = \sin \left( x ^ { 3 } \right)f(x)=sin(x3)

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