derivative of 5xe^{3x}

解答

\frac{d}{d x} (5 x e^{3 x})

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

求解步骤

\frac{d}{d x} (5 x e^{3 x})

将常数提出:

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

= 5 \frac{d}{d x} (x e^{3 x})

使用微分乘法定则:

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

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

= 5 (\frac{d x}{d x} e^{3 x} + \frac{d}{d x} (e^{3 x}) x)

\frac{d x}{d x} = 1

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

= 5 (1 \cdot e^{3 x} + e^{3 x} \cdot 3 x)

化简

= 5 (e^{3 x} + 3 e^{3 x} x)

\int_{0}^{\frac{π}{3}} 8 sec^{3} (x) d x

t an g e n t f (x) = 7 x + 2, (2, 4)

x y^{^{'}} + y = e^{x}, y (1) = 1

s l o p e in t erce pt (3, 6), (5, - 8)

\frac{\partial}{\partial x} (ln (x + t^{2}))