derivative of ,xe^y

解答

\frac{d}{d x} (, x e^{y})

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

求解步骤

\frac{d}{d x} (, x e^{y})

将常数提出:

(a \cdot f)^{'} = a \cdot f^{'}

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

使用微分乘法定则:

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

f = x, g = e^{y}

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

\frac{d x}{d x} = 1

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

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

t an g e n t ln (x^{2} - 24) = x - y + 6

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