derivative y=ln(1/(xsqrt(x+4)))

解答

导数

y = ln (\frac{1}{x x + 4})

- \frac{3 x + 8}{2 x ( x + 4 )}

求解步骤

\frac{d}{d x} (ln (\frac{1}{x x + 4}))

化简

ln (\frac{1}{x x + 4}) : - ln (x x + 4)

= \frac{d}{d x} (- ln (x x + 4))

将常数提出:

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

= - \frac{d}{d x} (ln (x x + 4))

使用连锁律:

\frac{1}{x x + 4} \frac{d}{d x} (x x + 4)

= \frac{1}{x x + 4} \frac{d}{d x} (x x + 4)

\frac{d}{d x} (x x + 4) = \frac{3 x + 8}{2 x + 4}

= - \frac{1}{x x + 4} \cdot \frac{3 x + 8}{2 x + 4}

化简

- \frac{1}{x x + 4} \cdot \frac{3 x + 8}{2 x + 4} : - \frac{3 x + 8}{2 x ( x + 4 )}

= - \frac{3 x + 8}{2 x ( x + 4 )}

d er i v a t i v e f (x) = x^{3}

p o l a r (- 43, - 4)

d er i v a t i v e x^{2} e^{x}

in t e g r a l e^{- 2 x}

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