(\partial)/(\partial x)((x+y)(2x+y)^2)

解答

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

12 x^{2} + 16 x y + 5 y^{2}

求解步骤

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

将

y

视为常数

使用微分乘法定则:

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

f = x + y, g = (2 x + y)^{2}

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

\frac{\partial}{\partial x} (x + y) = 1

\frac{\partial}{\partial x} ((2 x + y)^{2}) = 4 (2 x + y)

= 1 \cdot (2 x + y)^{2} + 4 (2 x + y) (x + y)

化简

1 \cdot (2 x + y)^{2} + 4 (2 x + y) (x + y) : 12 x^{2} + 16 x y + 5 y^{2}

= 12 x^{2} + 16 x y + 5 y^{2}

x \to + 0 lim (\frac{e ^{- 1 x} - 1}{x})

d er i v a t i v e y = x^{0.95}

d er i v a t i v e \frac{3 x}{x - 3}

\int_{0}^{1} y d y

x \to 0 - lim (- \frac{1}{x})