derivative of 3-ln(6x-(x^2)/(12)+x)

解答

\frac{d}{d x} (3 - ln (6 x) - \frac{x ^{2}}{12} + x)

- \frac{x}{6} - \frac{1}{x} + 1

求解步骤

\frac{d}{d x} (3 - ln (6 x) - \frac{x ^{2}}{12} + x)

使用微分加减法定则:

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

= \frac{d}{d x} (3) - \frac{d}{d x} (ln (6 x)) - \frac{d}{d x} (\frac{x ^{2}}{12}) + \frac{d x}{d x}

\frac{d}{d x} (3) = 0

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

\frac{d}{d x} (\frac{x ^{2}}{12}) = \frac{x}{6}

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

= 0 - \frac{1}{x} - \frac{x}{6} + 1

化简

= - \frac{x}{6} - \frac{1}{x} + 1