(\partial)/(\partial x)((1+2x^2)(x-x^2))

解答

\frac{\partial}{\partial x} ((1 + 2 x^{2}) (x - x^{2}))

- 8 x^{3} + 6 x^{2} - 2 x + 1

求解步骤

\frac{\partial}{\partial x} ((1 + 2 x^{2}) (x - x^{2}))

使用微分乘法定则:

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

f = 1 + 2 x^{2}, g = x - x^{2}

= \frac{\partial}{\partial x} (1 + 2 x^{2}) (x - x^{2}) + \frac{\partial}{\partial x} (x - x^{2}) (1 + 2 x^{2})

\frac{\partial}{\partial x} (1 + 2 x^{2}) = 4 x

\frac{\partial}{\partial x} (x - x^{2}) = 1 - 2 x

= 4 x (x - x^{2}) + (1 - 2 x) (1 + 2 x^{2})

化简

4 x (x - x^{2}) + (1 - 2 x) (1 + 2 x^{2}) : - 8 x^{3} + 6 x^{2} - 2 x + 1

= - 8 x^{3} + 6 x^{2} - 2 x + 1

s l o p e in t erce pt (7.2) (2.8)

\int_{- 6}^{6} 58

x \to 4 lim (\frac{∣ x ∣}{x})

\frac{d}{d x} (\frac{1}{2 + x ^{2}})

t an g e n t \frac{x ^{2}}{4 + x}