Find the differentiation of the following:sin2x with respect to ecosx.

1.	Find the differentiation of the following:sin2x with respect to ecosx.
Answer» Let y = sin²x & z = e^cosx \(\therefore\frac{dy}{dx}\) = 2 sin x cos x & \(\frac{dz}{dx}=-e^{cosx}\) sin x \(\frac{d(sin^2x)}{de^{cos x}}\) = \(\cfrac{\frac{dsin^2x}{dx}}{\frac{de^{cos x}}{dx}}\) = \(\cfrac{\frac{dy}{dx}}{\frac{dz}{dx}}\) = \(\frac{2sin xcos x}{-e^{cos x}sin x}\)

Answer»

Let y = sin²x & z = e^cosx

\(\therefore\frac{dy}{dx}\) = 2 sin x cos x

& \(\frac{dz}{dx}=-e^{cosx}\) sin x

\(\frac{d(sin^2x)}{de^{cos x}}\) = \(\cfrac{\frac{dsin^2x}{dx}}{\frac{de^{cos x}}{dx}}\) = \(\cfrac{\frac{dy}{dx}}{\frac{dz}{dx}}\) = \(\frac{2sin xcos x}{-e^{cos x}sin x}\)

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Find the differentiation of the following:sin2x with respect to ecosx.

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