derivative of cos(e^{-5x^5})

解答

\frac{d}{d x} (cos (e^{- 5 x^{5}}))

25 e^{- 5 x^{5}} x^{4} sin (e^{- 5 x^{5}})

求解步骤

\frac{d}{d x} (cos (e^{- 5 x^{5}}))

使用连锁律:

- sin (e^{- 5 x^{5}}) \frac{d}{d x} (e^{- 5 x^{5}})

= - sin (e^{- 5 x^{5}}) \frac{d}{d x} (e^{- 5 x^{5}})

\frac{d}{d x} (e^{- 5 x^{5}}) = - 25 e^{- 5 x^{5}} x^{4}

= - sin (e^{- 5 x^{5}}) (- 25 e^{- 5 x^{5}} x^{4})

化简

= 25 e^{- 5 x^{5}} x^{4} sin (e^{- 5 x^{5}})

\int \frac{8 + tan ( x )}{1 - sin ^{2} ( x )} d x

\int \frac{4}{t ^{2}} d t

t an g e n t 22 x^{3}

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

x \to 2 lim (sin (x))