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Q. If $y = (\cos \, x^2)^2$ then $\frac{dy}{dx}$ is equal to:

Continuity and Differentiability

Solution:

As given : $y = (\cos\, x^2)^2$
Diff both side w.r.t 'x'
$\frac{dy}{dx} = 2 \, \cos \, x^2 (-\sin\, x^2)2x$
$ = - 4 x \, \cos \, x^2 \, \sin \, x^2$
$ = - 2x (2 \, \sin \, x^2 \, \cos \, x^2)$
$(\because \: \sin \, 2 \theta = 2 \, \sin \, \theta \, \cos \, \theta)$
$ = - 2x \, \sin \, 2x^2$