derivative y=arctan(e^x)

解答

导数

y = arctan (e^{x})

\frac{e ^{x}}{e ^{2 x} + 1}

求解步骤

\frac{d}{d x} (arctan (e^{x}))

使用连锁律:

\frac{1}{( e ^{x} ) ^{2} + 1} \frac{d}{d x} (e^{x})

= \frac{1}{( e ^{x} ) ^{2} + 1} \frac{d}{d x} (e^{x})

\frac{d}{d x} (e^{x}) = e^{x}

= \frac{1}{( e ^{x} ) ^{2} + 1} e^{x}

化简

\frac{1}{( e ^{x} ) ^{2} + 1} e^{x} : \frac{e ^{x}}{e ^{2 x} + 1}

= \frac{e ^{x}}{e ^{2 x} + 1}

\int 3 x^{2} - 6 x d x

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