derivative of ((4x^2/(8-x))^3)

解答

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

\frac{192 x ^{4} ( 16 x - x ^{2} )}{( 8 - x ) ^{4}}

求解步骤

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

使用连锁律:

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

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

\frac{d}{d x} (\frac{4 x ^{2}}{8 - x}) = \frac{4 ( 16 x - x ^{2} )}{( 8 - x ) ^{2}}

= 3 (\frac{4 x ^{2}}{8 - x})^{2} \frac{4 ( 16 x - x ^{2} )}{( 8 - x ) ^{2}}

化简

3 (\frac{4 x ^{2}}{8 - x})^{2} \frac{4 ( 16 x - x ^{2} )}{( 8 - x ) ^{2}} : \frac{192 x ^{4} ( 16 x - x ^{2} )}{( 8 - x ) ^{4}}

= \frac{192 x ^{4} ( 16 x - x ^{2} )}{( 8 - x ) ^{4}}

x \to 1 lim (\frac{x ^{3} + 1}{x - 1})

\frac{\partial}{\partial y} (\frac{y ^{2}}{x + 1})

d er i v a t i v e 3 sin (θ)

in v erse l a pl a ce f (s) = \frac{2}{( 4 s ^{2} - 8 s )}

\frac{\partial}{\partial x} (x^{0.6} \cdot y^{0.4})