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

Question

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

Quizplus · Accepted Answer

To find the derivative of $f(x) = x^2 \cos x$, we use the product rule: $(uv)' = u'v + uv'$. Here, $u = x^2$ and $v = \cos x$, so $u' = 2x$ and $v' = -\sin x$. Applying the product rule, we get $f'(x) = 2x \cos x + x^2(-\sin x) = 2x \cos x - x^2 \sin x$.

Find the Derivative Of f(x)=x2cos⁡xf ( x ) = x ^ { 2 } \cos xf(x)=x2cosx

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