derivative of (1+e^x^4)

解答

\frac{d}{d x} ((1 + e^{x})^{4})

4 (1 + e^{x})^{3} e^{x}

求解步骤

\frac{d}{d x} ((1 + e^{x})^{4})

使用连锁律:

4 (1 + e^{x})^{3} \frac{d}{d x} (1 + e^{x})

= 4 (1 + e^{x})^{3} \frac{d}{d x} (1 + e^{x})

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

= 4 (1 + e^{x})^{3} e^{x}

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