Differentiate.
-$( \sin 3 t ) ^ { 2 }$
A) 6 sin 3t cos 3t
B) 6 sin 3t
C) 2 sin 3t cos 3t
D) 2 sin 3t
E) none of these

Question

Quizplus · Accepted Answer

The differentiation of $(\sin 3t)^2$ with respect to $t$ can be found using the chain rule and the derivative of $\sin x$, which is $\cos x$. First, let $u = \sin 3t$, so we have $u^2$. The derivative of $u^2$ with respect to $u$ is $2u$, and the derivative of $u = \sin 3t$ with respect to $t$ is $3\cos 3t$. Applying the chain rule, we get $2(\sin 3t)(3\cos 3t) = 6\sin 3t \cos 3t$.

Differentiate (sin⁡3t)2( \sin 3 t ) ^ { 2 }(sin3t)2 A) 6 Sin 3t Cos 3t B) 6 Sin 3t

Differentiate $( \sin 3 t ) ^ { 2 }$ A) 6 Sin 3t Cos 3t
B) 6 Sin 3t