Question

d/dx sin^2(2x^4)

Answer 1

\[ \frac{d}{dx}\sin^2(2x^4)\]
Think of this as \[ \frac{d}{dx}(\sin(2x^4))^2\]
And so by the chain rule. this gives \[ 2(\sin(2x^4))^1\cdot \frac{d}{dx}\sin(2x^4)\]
By the chain rule again, \[ \frac{d}{dx}\sin(2x^4)=\cos(2x^4)\cdot \frac{d}{dx}(2x^4)\]
And by the power rule \[ \frac{d}{dx}(2x^4)=2(4)x^3\]

Answer 2

combine those results and simplify