derivative of-3x^6ln(x)

解答

\frac{d}{d x} (- 3 x^{6} ln (x))

- 3 (6 x^{5} ln (x) + x^{5})

求解步骤

\frac{d}{d x} (- 3 x^{6} ln (x))

将常数提出:

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

= - 3 \frac{d}{d x} (x^{6} ln (x))

使用微分乘法定则:

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

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

= - 3 (\frac{d}{d x} (x^{6}) ln (x) + \frac{d}{d x} (ln (x)) x^{6})

\frac{d}{d x} (x^{6}) = 6 x^{5}

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

= - 3 (6 x^{5} ln (x) + \frac{1}{x} x^{6})

\frac{1}{x} x^{6} = x^{5}

= - 3 (6 x^{5} ln (x) + x^{5})

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