derivative x^2e^{3x}

解答

导数

x^{2} e^{3 x}

2 x e^{3 x} + e^{3 x} \cdot 3 x^{2}

求解步骤

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

使用微分乘法定则:

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

f = x^{2}, g = e^{3 x}

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

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

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

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

in t e g r a l x

d er i v a t i v e f (x) = 3 x + 8, at x = 4

s l o p e (8.4) (20.1)

s l o p e y = 2 x + 3

t an g e n t x^{2} + y^{2} + 2 x y = 4, (1, 1)