Differentiate.
-sin $x ^ { 5 }$
A) 5 $x ^ { 4 }$ cos $x ^ { 5 }$
B) 5 $( \sin x ) ^ { 4 }$ cos x
C) 5 sin $x ^ { 4 }$
D) 5x cos $x ^ { 5 }$

Question

Quizplus · Accepted Answer

The differentiation of $sin(x^5)$ with respect to $x$ is done using the chain rule. The outer function is $sin(u)$, where $u = x^5$, and its derivative is $cos(u)$. The derivative of the inner function $u = x^5$ with respect to $x$ is $5x^4$. Applying the chain rule, the derivative is $cos(x^5) \cdot 5x^4$, which simplifies to $5x^4 cos(x^5)$.

Differentiate x5x ^ { 5 }x5 A) 5 x4x ^ { 4 }x4

Differentiate $x ^ { 5 }$ A) 5 $x ^ { 4 }$