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

解答

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

- 4 x^{3} + 24 x^{2} - 44 x + 24

求解步骤

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

将常数提出:

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

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

使用微分乘法定则:

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

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

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

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

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

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

化简

- (2 (x - 3) (1 - x)^{2} + (- 2 (1 - x)) (x - 3)^{2}) : - 4 x^{3} + 24 x^{2} - 44 x + 24

= - 4 x^{3} + 24 x^{2} - 44 x + 24

\frac{\partial}{\partial x} ((4 x + 4) (ln (8 x y)))

\frac{d}{d x} (A x^{2} e^{- 2 x})

\int (sec^{2} (x) - 5) d x

t an g e n t f (x) = (1 + 5 x)^{9}, at x = 0

x \to 0 + lim (\frac{I n x}{x})