derivative of y(e^x-1)

解答

\frac{d}{d x} (y (e^{x} - 1))

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

求解步骤

\frac{d}{d x} (y (e^{x} - 1))

使用微分乘法定则:

(f \cdot g)^{'} = f^{'} \cdot g + f \cdot g^{'}

f = y, g = e^{x} - 1

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

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

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

\int (\frac{x}{5})^{n} d x

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