derivative 6(2e^{x^2}x^2+e^{x^2})

解答

导数

6 (2 e^{x^{2}} x^{2} + e^{x^{2}})

6 (4 e^{x^{2}} x^{3} + 6 e^{x^{2}} x)

求解步骤

\frac{d}{d x} (6 (2 e^{x^{2}} x^{2} + e^{x^{2}}))

将常数提出:

(a \cdot f)^{'} = a \cdot f^{'}

= 6 \frac{d}{d x} (2 e^{x^{2}} x^{2} + e^{x^{2}})

使用微分加减法定则:

(f \pm g)^{'} = f^{'} \pm g^{'}

= 6 (\frac{d}{d x} (2 e^{x^{2}} x^{2}) + \frac{d}{d x} (e^{x^{2}}))

\frac{d}{d x} (2 e^{x^{2}} x^{2}) = 2 (2 e^{x^{2}} x^{3} + 2 e^{x^{2}} x)

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

= 6 (2 (2 e^{x^{2}} x^{3} + 2 e^{x^{2}} x) + e^{x^{2}} \cdot 2 x)

乘开

2 (2 e^{x^{2}} x^{3} + 2 e^{x^{2}} x) + e^{x^{2}} \cdot 2 x : 4 e^{x^{2}} x^{3} + 6 e^{x^{2}} x

= 6 (4 e^{x^{2}} x^{3} + 6 e^{x^{2}} x)

d er i v a t i v e 3 + x

x \to + 0 + lim (ln (2 x))

\int_{1}^{2} \frac{x}{2} d x

\int t t^{2} + 2 d t

\int \frac{y}{x} d x