derivative of 12x^3+4-ln(3x+7)

解答

\frac{d}{d x} (12 x^{3} + 4 - ln (3 x + 7))

36 x^{2} - \frac{3}{3 x + 7}

求解步骤

\frac{d}{d x} (12 x^{3} + 4 - ln (3 x + 7))

使用微分加减法定则:

(f \pm g)^{'} = f^{'} \pm g^{'}

= \frac{d}{d x} (12 x^{3}) + \frac{d}{d x} (4) - \frac{d}{d x} (ln (3 x + 7))

\frac{d}{d x} (12 x^{3}) = 36 x^{2}

\frac{d}{d x} (4) = 0

\frac{d}{d x} (ln (3 x + 7)) = \frac{3}{3 x + 7}

= 36 x^{2} + 0 - \frac{3}{3 x + 7}

化简

= 36 x^{2} - \frac{3}{3 x + 7}

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