derivative of-1/(3\sqrt[5]{7cos(2x)})

解答

\frac{d}{d x} (- \frac{1}{3 5 7 cos ( 2 x )})

- \frac{2 sin ( 2 x )}{15 5 7 cos ^{\frac{6}{5}} ( 2 x )}

求解步骤

\frac{d}{d x} (- \frac{1}{3 5 7 cos ( 2 x )})

化简

- \frac{1}{3 5 7 cos ( 2 x )} : - \frac{1}{3 5 7 5 cos ( 2 x )}

= \frac{d}{d x} (- \frac{1}{3 5 7 5 cos ( 2 x )})

将常数提出:

(a \cdot f)^{'} = a \cdot f^{'}

= - \frac{1}{3 5 7} \frac{d}{d x} (\frac{1}{5 cos ( 2 x )})

使用指数法则:

\frac{1}{a} = a^{- 1}

= - \frac{1}{3 5 7} \frac{d}{d x} (cos^{- \frac{1}{5}} (2 x))

使用连锁律:

- \frac{1}{5 ( cos ( 2 x ) ) ^{\frac{6}{5}}} \frac{d}{d x} (cos (2 x))

= - \frac{1}{5 ( cos ( 2 x ) ) ^{\frac{6}{5}}} \frac{d}{d x} (cos (2 x))

\frac{d}{d x} (cos (2 x)) = - sin (2 x) \cdot 2

= - \frac{1}{3 5 7} (- \frac{1}{5 ( cos ( 2 x ) ) ^{\frac{6}{5}}} (- sin (2 x) \cdot 2))

化简

- \frac{1}{3 5 7} (- \frac{1}{5 cos ^{\frac{6}{5}} ( 2 x )} (- sin (2 x) \cdot 2)) : - \frac{2 sin ( 2 x )}{15 5 7 cos ^{\frac{6}{5}} ( 2 x )}

= - \frac{2 sin ( 2 x )}{15 5 7 cos ^{\frac{6}{5}} ( 2 x )}

\frac{d}{d x} ((5 x + 3)^{4})

\frac{d}{d x} ((arctan (7 x))^{2})

x \to a lim (\frac{3 x - 3 a}{x ^{2} - a ^{2}})

y = 0 \sum \infty 2^{- 2 - y + x}

\frac{\partial}{\partial y} (x 1 + y^{5})