derivative of xln(x^{18})

解答

\frac{d}{d x} (x ln (x^{18}))

18 ln (x) + 18

求解步骤

\frac{d}{d x} (x ln (x^{18}))

使用微分乘法定则:

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

f = x, g = ln (x^{18})

= \frac{d x}{d x} ln (x^{18}) + \frac{d}{d x} (ln (x^{18})) x

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

\frac{d}{d x} (ln (x^{18})) = \frac{18}{x}

= 1 \cdot ln (x^{18}) + \frac{18}{x} x

化简

1 \cdot ln (x^{18}) + \frac{18}{x} x : 18 ln (x) + 18

= 18 ln (x) + 18

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