Question

calculate the derivative of the following function y=cos^2(2x-pi)

Answer 1

given

$=>y=\cos^{2} (2x-\pi )$

differentiating both sides with respect to x

$=> \frac{dy}{dx} =\frac{d}{dx}( \cos^{2}(2x- \pi )\\\\=>\frac{dy}{dx} =2\cos(2x-\pi )*\frac{d}{dx} (\cos(2x-\pi)\\\\=>\frac{dy}{dx} =2\cos(2x-\pi )*[-\sin(2x-\pi )]*\frac{d}{dx} (2x-\pi )\\\\=>\frac{dy}{dx} =-\sin2(2x-\pi)*2*\frac{dx}{dx} =-2\sin(4x-2\pi )\\\\\\since\\\\=>2\sin(x)\cos(x)=\sin(2x)$

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