derivative of sqrt(ln(-5x+2x^{-2)})

解答

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

\frac{- 5 x ^{3} - 4}{2 x ( - 5 x ^{3} + 2 ) ln ( - 5 x ^{3} + 2 ) - 2 ln ( x )}

求解步骤

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

使用连锁律:

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

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

\frac{d}{d x} (ln (- 5 x + 2 x^{- 2})) = \frac{- 5 x ^{3} - 4}{x ( - 5 x ^{3} + 2 )}

= \frac{1}{2 ln ( - 5 x + 2 x ^{- 2} )} \cdot \frac{- 5 x ^{3} - 4}{x ( - 5 x ^{3} + 2 )}

化简

\frac{1}{2 ln ( - 5 x + 2 x ^{- 2} )} \cdot \frac{- 5 x ^{3} - 4}{x ( - 5 x ^{3} + 2 )} : \frac{- 5 x ^{3} - 4}{2 x ( - 5 x ^{3} + 2 ) ln ( - 5 x ^{3} + 2 ) - 2 ln ( x )}

= \frac{- 5 x ^{3} - 4}{2 x ( - 5 x ^{3} + 2 ) ln ( - 5 x ^{3} + 2 ) - 2 ln ( x )}

\frac{d}{d x} (x e^{x^{2} - y})

d er i v a t i v e (1 + t) (2 t^{2} - 7)

\int \frac{4}{1 - x ^{2}} d x

d er i v a t i v e sin (3 ln (x))

\frac{\partial}{\partial x} (3 ln (x + y) - 3 x)