derivative (x^3+3)e^x

解答

导数

(x^{3} + 3) e^{x}

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

求解步骤

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

使用微分乘法定则:

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

f = x^{3} + 3, g = e^{x}

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

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

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

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

n = 1 \sum \infty \frac{1}{( n ( n + 3 ) )}

\int 1 - 2 x d x

d er i v a t i v e a^{2} + 2 a + 2

\frac{d}{d x} (sech (2 x))

\frac{\partial}{\partial x} ((3 x + 2 y)^{5})