derivative 8x^4ln(6x)

解答

导数

8 x^{4} ln (6 x)

8 (4 x^{3} ln (6 x) + x^{3})

求解步骤

\frac{d}{d x} (8 x^{4} ln (6 x))

将常数提出:

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

= 8 \frac{d}{d x} (x^{4} ln (6 x))

使用微分乘法定则:

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

f = x^{4}, g = ln (6 x)

= 8 (\frac{d}{d x} (x^{4}) ln (6 x) + \frac{d}{d x} (ln (6 x)) x^{4})

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

\frac{d}{d x} (ln (6 x)) = \frac{1}{x}

= 8 (4 x^{3} ln (6 x) + \frac{1}{x} x^{4})

\frac{1}{x} x^{4} = x^{3}

= 8 (4 x^{3} ln (6 x) + x^{3})

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