derivative f(x)=3e^{2x^2}

解答

导数

f (x) = 3 e^{2 x^{2}}

12 e^{2 x^{2}} x

求解步骤

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

将常数提出:

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

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

使用连锁律:

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

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

\frac{d}{d x} (2 x^{2}) = 4 x

= 3 e^{2 x^{2}} \cdot 4 x

化简

= 12 e^{2 x^{2}} x

\int_{- 2}^{0} (5 x^{2} + 5 x) d x

x \to \infty lim (5 x^{3})

\frac{d}{d x} (\frac{2 x + 1}{x - 1})

\frac{d}{d x} (\frac{y}{x})

\frac{d}{d x} (arcsin (\frac{a x}{4}))