derivative of sqrt(log_{a)(-x^2-x})

解答

\frac{d}{d x} (lo g_{a} (- x^{2} - x))

\frac{- 2 x - 1}{2 ln ( a ) lo g _{a} ( - x ^{2} - x ) ( - x ^{2} - x )}

求解步骤

\frac{d}{d x} (lo g_{a} (- x^{2} - x))

使用连锁律:

\frac{1}{2 lo g _{a} ( - x ^{2} - x )} \frac{d}{d x} (lo g_{a} (- x^{2} - x))

= \frac{1}{2 lo g _{a} ( - x ^{2} - x )} \frac{d}{d x} (lo g_{a} (- x^{2} - x))

\frac{d}{d x} (lo g_{a} (- x^{2} - x)) = \frac{- 2 x - 1}{ln ( a ) ( - x ^{2} - x )}

= \frac{1}{2 lo g _{a} ( - x ^{2} - x )} \cdot \frac{- 2 x - 1}{ln ( a ) ( - x ^{2} - x )}

化简

\frac{1}{2 lo g _{a} ( - x ^{2} - x )} \cdot \frac{- 2 x - 1}{ln ( a ) ( - x ^{2} - x )} : \frac{- 2 x - 1}{2 ln ( a ) lo g _{a} ( - x ^{2} - x ) ( - x ^{2} - x )}

= \frac{- 2 x - 1}{2 ln ( a ) lo g _{a} ( - x ^{2} - x ) ( - x ^{2} - x )}

\frac{d}{d x} ((e^{3 x} - 1)^{5})

d er i v a t i v e y = ln (ln (\frac{1}{x}))

t an g e n t f (x) = 2 x^{2} + 8 x - 2

d er i v a t i v e \frac{7}{x ^{2}}

x \to \infty lim (\frac{4 ^{x}}{5 ^{x + 1}})