derivative of xe^{x^4}

解答

\frac{d}{d x} (x e^{x^{4}})

e^{x^{4}} + 4 e^{x^{4}} x^{4}

求解步骤

\frac{d}{d x} (x e^{x^{4}})

使用微分乘法定则:

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

f = x, g = e^{x^{4}}

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

\frac{d x}{d x} = 1

\frac{d}{d x} (e^{x^{4}}) = e^{x^{4}} \cdot 4 x^{3}

= 1 \cdot e^{x^{4}} + e^{x^{4}} \cdot 4 x^{3} x

化简

1 \cdot e^{x^{4}} + e^{x^{4}} \cdot 4 x^{3} x : e^{x^{4}} + 4 e^{x^{4}} x^{4}

= e^{x^{4}} + 4 e^{x^{4}} x^{4}

\frac{d}{d z} (x^{2} y z)

\int x^{5} \cdot ln (x) d x

y^{^{''}} + 9 y = 19

d er i v a t i v e f (x) = \frac{x ^{2}}{8 - 8 x}

d er i v a t i v e (\frac{1}{y ^{2}} - \frac{5}{y ^{4}}) (y + 9 y^{3})