derivative of ln(x^4sqrt(8-6x))

解答

\frac{d}{d x} (ln (x^{4} 8 - 6 x))

\frac{- 27 x + 32}{2 x ( - 3 x + 4 )}

求解步骤

\frac{d}{d x} (ln (x^{4} 8 - 6 x))

使用连锁律:

\frac{1}{x ^{4} 8 - 6 x} \frac{d}{d x} (x^{4} 8 - 6 x)

= \frac{1}{x ^{4} 8 - 6 x} \frac{d}{d x} (x^{4} 8 - 6 x)

\frac{d}{d x} (x^{4} 8 - 6 x) = \frac{- 27 x ^{4} + 32 x ^{3}}{8 - 6 x}

= \frac{1}{x ^{4} 8 - 6 x} \cdot \frac{- 27 x ^{4} + 32 x ^{3}}{8 - 6 x}

化简

\frac{1}{x ^{4} 8 - 6 x} \cdot \frac{- 27 x ^{4} + 32 x ^{3}}{8 - 6 x} : \frac{- 27 x + 32}{2 x ( - 3 x + 4 )}

= \frac{- 27 x + 32}{2 x ( - 3 x + 4 )}

d er i v a t i v e g (x) = \frac{1 - 3 x}{5 + x}

d er i v a t i v e tan^{2} (4 x)

n \to \infty lim ((- 1)^{n})

\frac{d}{d x} (\frac{x ^{3}}{3 - 6 x ^{2} + 8 x - 7})

\frac{d}{d x} (\frac{20 x ^{2}}{( x - 1 ) ^{3}})