derivative of (4x+1^2(1-x)^3)

解答

\frac{d}{d x} ((4 x + 1)^{2} (1 - x)^{3})

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

求解步骤

\frac{d}{d x} ((4 x + 1)^{2} (1 - x)^{3})

使用微分乘法定则:

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

f = (4 x + 1)^{2}, g = (1 - x)^{3}

= \frac{d}{d x} ((4 x + 1)^{2}) (1 - x)^{3} + \frac{d}{d x} ((1 - x)^{3}) (4 x + 1)^{2}

\frac{d}{d x} ((4 x + 1)^{2}) = 8 (4 x + 1)

\frac{d}{d x} ((1 - x)^{3}) = - 3 (1 - x)^{2}

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

化简

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

x \to 0 lim (\frac{x + 1}{x + 4})

(\frac{d y}{d x}) = \frac{( 2 x ( y - 1 ) )}{x ^{2} + 3}

y^{2} + 1 d x = x y d y

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

\int_{0}^{3} - x^{2} d x