derivative sqrt(35x)ln(20x)

解答

导数

35 x ln (20 x)

\frac{35 ln ( 20 x )}{2 x} + \frac{35}{x}

求解步骤

\frac{d}{d x} (35 x ln (20 x))

使用微分乘法定则:

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

f = 35 x, g = ln (20 x)

= \frac{d}{d x} (35 x) ln (20 x) + \frac{d}{d x} (ln (20 x)) 35 x

\frac{d}{d x} (35 x) = \frac{35}{2 x}

\frac{d}{d x} (ln (20 x)) = \frac{1}{x}

= \frac{35}{2 x} ln (20 x) + \frac{1}{x} 35 x

化简

\frac{35}{2 x} ln (20 x) + \frac{1}{x} 35 x : \frac{35 ln ( 20 x )}{2 x} + \frac{35}{x}

= \frac{35 ln ( 20 x )}{2 x} + \frac{35}{x}

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