derivative of 1/4 e^{2x^2}

解答

\frac{d}{d x} (\frac{1}{4} e^{2 x^{2}})

e^{2 x^{2}} x

求解步骤

\frac{d}{d x} (\frac{1}{4} e^{2 x^{2}})

将常数提出:

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

= \frac{1}{4} \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

= \frac{1}{4} e^{2 x^{2}} \cdot 4 x

化简

\frac{1}{4} e^{2 x^{2}} \cdot 4 x : e^{2 x^{2}} x

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

y^{^{''}} - 4 y^{^{'}} + 2 y = 0

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

\int x (1 + x)^{\frac{1}{4}} d x

d er i v a t i v e f (x) = \frac{e ^{x}}{x ^{2} + 4}, x = 1

t an g e n t x^{4} - 3 x^{3} + 2 x^{2} - x + 1