derivative y=xe^{x^2}

解答

导数

y = x e^{x^{2}}

e^{x^{2}} + 2 e^{x^{2}} x^{2}

求解步骤

\frac{d}{d x} (x e^{x^{2}})

使用微分乘法定则:

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

f = x, g = e^{x^{2}}

= \frac{d x}{d x} e^{x^{2}} + \frac{d}{d x} (e^{x^{2}}) x

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

\frac{d}{d x} (e^{x^{2}}) = e^{x^{2}} \cdot 2 x

= 1 \cdot e^{x^{2}} + e^{x^{2}} \cdot 2 xx

化简

1 \cdot e^{x^{2}} + e^{x^{2}} \cdot 2 xx : e^{x^{2}} + 2 e^{x^{2}} x^{2}

= e^{x^{2}} + 2 e^{x^{2}} x^{2}

\frac{d}{d x} (\frac{3 x - 9}{x + 5})

\int (π - x) \cdot cos (n x) d x

\int \frac{x ^{2}}{( x ^{3} - 5 ) ^{2}} d x

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

y^{^{'}} + y = e^{2 t}, y (0) = - 1