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Differentiate the following functions...

Differentiate the following functions with respect to `(2^xcosx)/((x^2+3)^2)`

Text Solution

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Let `y=(2^xcosx)/((x^2+3)^2)`
`(dy)/(dx)=frac{d}{d x}(frac{2^{x} cos x}{(x^{2}+3)^{2}})`

`=frac{(frac{d}{d x}(2^{x} cos x))(x^{2}+3)^{2}-4 x(x^{2}+3)(2^{x} cos x)}{(x^{2}+3)^{4}}`

`=frac{(2^{x} ln 2 cos x-sin x(2^{x}))(x^{2}+3)^{2}-4 x(x^{2}+3)(2^{x} cos x)}{(x^{2}+3)^{4}}`

`=frac{2^{x}}{(x^{2}+3)^{4}}{cos x cdot log _{e} 2-sin x-frac{4 x cos x}{x^{2}+3}}`

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