Answer
$\frac{d}{dx}sin(x^2) = 2cos(x^2)-4x^2sin(x^2)$
Work Step by Step
Chain Rule
$\frac{d}{dx}[f(g(x))] = f'(g(x)) \times g'(x)$
$y=sin(x^2)$
Chain Rule:
$\frac{d}{dx}[sin(x^2)] = 2xcos(x^2)$
Product Rule and Chain Rule:
$\frac{d}{dx}[2xcos(x^2)] = (\frac{d}{dx}2x)(cos(x^2)) + (2x)(\frac{d}{dx}(cos(x^2)) = 2cos(x^2)+2x(2x(-sin(x^2)) = 2cos(x^2)-4x^2sin(x^2)$
