derivative 4^{-x^8}

解答

导数

4^{- x^{8}}

- ln (2) \cdot 2^{- 2 x^{8} + 4} x^{7}

求解步骤

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

使用指数法则:

a^{b} = e^{b l n (a)}

4^{- x^{8}} = e^{(- x^{8}) l n (4)}

= \frac{d}{d x} (e^{(- x^{8}) l n (4)})

使用连锁律:

e^{(- x^{8}) l n (4)} \frac{d}{d x} ((- x^{8}) ln (4))

= e^{(- x^{8}) l n (4)} \frac{d}{d x} ((- x^{8}) ln (4))

\frac{d}{d x} ((- x^{8}) ln (4)) = - 16 ln (2) x^{7}

= e^{(- x^{8}) l n (4)} (- 16 ln (2) x^{7})

化简

e^{(- x^{8}) l n (4)} (- 16 ln (2) x^{7}) : - ln (2) \cdot 2^{- 2 x^{8} + 4} x^{7}

= - ln (2) \cdot 2^{- 2 x^{8} + 4} x^{7}

\int 2 sin^{2} (x) d x

x^{3} + y^{2} x^{4} + 4 y^{^{'}} = 0

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

\frac{d}{d x} (\frac{f ( x )}{g ( x ) - 2})

im pl i c i t \frac{d y}{d x}, 3 x y + 1 = 0