derivative of x^6e^{8x}

解答

\frac{d}{d x} (x^{6} e^{8 x})

6 x^{5} e^{8 x} + e^{8 x} \cdot 8 x^{6}

求解步骤

\frac{d}{d x} (x^{6} e^{8 x})

使用微分乘法定则:

(f \cdot g)^{'} = f^{'} \cdot g + f \cdot g^{'}

f = x^{6}, g = e^{8 x}

= \frac{d}{d x} (x^{6}) e^{8 x} + \frac{d}{d x} (e^{8 x}) x^{6}

\frac{d}{d x} (x^{6}) = 6 x^{5}

\frac{d}{d x} (e^{8 x}) = e^{8 x} \cdot 8

= 6 x^{5} e^{8 x} + e^{8 x} \cdot 8 x^{6}

\int \frac{x + 2}{x ^{2} - 2 x + 10} d x

d er i v a t i v e (\frac{4}{5} x)^{4}

\frac{\partial}{\partial x} (x - w)

x y^{^{'}} + 4 y = \frac{2 e ^{- 4 x}}{x ^{3}}

t an g e n t y = - 3 x^{2} + 10 x + 2, at x = 1