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Find the derivative of ecos2x

Find the derivative of the following function:

    \[ f(x) = e^{\cos^2 x}. \]


Using the chain rule and the formula for the derivative of the exponential we have,

    \[ f'(x) = (\cos^2 x)' e^{\cos^2 x} = -2 \sin x \cos x e^{\cos^2x } = -\sin(2x) e^{\cos^2 x}. \]

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