derivative of ln((x^2/5+9/x))

解答

\frac{d}{d x} (ln (\frac{x ^{2}}{5} + \frac{9}{x}))

\frac{2 x ^{3} - 45}{x ( x ^{3} + 45 )}

求解步骤

\frac{d}{d x} (ln (\frac{x ^{2}}{5} + \frac{9}{x}))

使用连锁律:

\frac{1}{\frac{x ^{2}}{5} + \frac{9}{x}} \frac{d}{d x} (\frac{x ^{2}}{5} + \frac{9}{x})

= \frac{1}{\frac{x ^{2}}{5} + \frac{9}{x}} \frac{d}{d x} (\frac{x ^{2}}{5} + \frac{9}{x})

\frac{d}{d x} (\frac{x ^{2}}{5} + \frac{9}{x}) = \frac{2 x}{5} - \frac{9}{x ^{2}}

= \frac{1}{\frac{x ^{2}}{5} + \frac{9}{x}} (\frac{2 x}{5} - \frac{9}{x ^{2}})

化简

\frac{1}{\frac{x ^{2}}{5} + \frac{9}{x}} (\frac{2 x}{5} - \frac{9}{x ^{2}}) : \frac{2 x ^{3} - 45}{x ( x ^{3} + 45 )}

= \frac{2 x ^{3} - 45}{x ( x ^{3} + 45 )}

t an g e n t y = 2 x^{2} - x, (1, 1)

\frac{d}{d x} (5 x + \frac{7}{x})

\int_{1}^{5} \frac{ln ( x )}{x ^{5}} d x

d er i v a t i v e f (x) = 4 x^{3} - 11 x^{2} - 14 x + 19

x \to 0 lim ((\frac{1 + tan ( x )}{1 + sin ( x )})^{\frac{1}{s i n ( x )}})