How do you find the derivative of ${cos}^{2} x$ $cos^2x$ ?

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Answer 1 · 2016-03-26T19:37:15

$\frac{d}{d x} {cos}^{2} x = - 2 sin x cos x$ $d/dxcos^2x=-2sinxcosx$

By using the power rule together with standard differentiation rules, we get

$\frac{d}{d x} {cos}^{2} x = \frac{d}{d x} {[cos x]}^{2}$ $d/dxcos^2 x=d/dx[cosx]^2$

$= 2 {(cos x)}^{1} \cdot \frac{d}{d x} cos x$ $=2(cosx)^1 *d/dxcosx$

$= 2 cos x \cdot (- sin x)$ $=2cosx*(-sinx)$

$= - 2 sin x cos x$ $=-2sinxcosx$

How do you find the derivative of cos2xcos^2x?