Answer
$$ u=\cos x^{2}\Longrightarrow du =-2x \sin x^2 dx .$$
Work Step by Step
Recall that $(\cos x)'=-\sin x$.
Recall that $(x^n)'=nx^{n-1}$
$$ u=\cos x^{2}\Longrightarrow du =-2x \sin x^2 dx .$$
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