derivative of ((x-7/(x+2))^3)

解答

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

\frac{27 ( x - 7 ) ^{2}}{( x + 2 ) ^{4}}

求解步骤

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

使用连锁律:

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

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

\frac{d}{d x} (\frac{x - 7}{x + 2}) = \frac{9}{( x + 2 ) ^{2}}

= 3 (\frac{x - 7}{x + 2})^{2} \frac{9}{( x + 2 ) ^{2}}

化简

3 (\frac{x - 7}{x + 2})^{2} \frac{9}{( x + 2 ) ^{2}} : \frac{27 ( x - 7 ) ^{2}}{( x + 2 ) ^{4}}

= \frac{27 ( x - 7 ) ^{2}}{( x + 2 ) ^{4}}

\int \frac{1}{x - 3 3 x} d x

d er i v a t i v e y = \frac{8 - x e ^{x}}{x + e ^{x}}

\frac{\partial}{\partial x} (\frac{2 F ( V , x , P )}{V ^{2} x P})

\frac{d ^{3}}{d x ^{3}} (\frac{5}{x})

d er i v a t i v e y = (3 x^{6} - 2 x^{4})^{4}