derivative of ((x+3/(x-3))^4)

解答

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

- \frac{24 ( x + 3 ) ^{3}}{( x - 3 ) ^{5}}

求解步骤

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

使用连锁律:

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

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

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

= 4 (\frac{x + 3}{x - 3})^{3} (- \frac{6}{( x - 3 ) ^{2}})

化简

4 (\frac{x + 3}{x - 3})^{3} (- \frac{6}{( x - 3 ) ^{2}}) : - \frac{24 ( x + 3 ) ^{3}}{( x - 3 ) ^{5}}

= - \frac{24 ( x + 3 ) ^{3}}{( x - 3 ) ^{5}}

\frac{\partial}{\partial x} (\frac{y - z}{x})

\int_{0}^{1} (x - x)^{2} d x

in v erse l a pl a ce \frac{s - 4}{s ^{2} - 8 s + 10}

d er i v a t i v e t^{\frac{4}{3}}

t an g e n t f (x) = x^{3} - 9 x + 4, (3, 4)