derivative of x(12-2x^2)

解答

\frac{d}{d x} (x (12 - 2 x)^{2})

12 x^{2} - 96 x + 144

求解步骤

\frac{d}{d x} (x (12 - 2 x)^{2})

使用微分乘法定则:

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

f = x, g = (12 - 2 x)^{2}

= \frac{d x}{d x} (12 - 2 x)^{2} + \frac{d}{d x} ((12 - 2 x)^{2}) x

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

\frac{d}{d x} ((12 - 2 x)^{2}) = - 4 (12 - 2 x)

= 1 \cdot (12 - 2 x)^{2} + (- 4 (12 - 2 x)) x

化简

1 \cdot (12 - 2 x)^{2} + (- 4 (12 - 2 x)) x : 12 x^{2} - 96 x + 144

= 12 x^{2} - 96 x + 144

\int 8 e^{4 x} cos (6 x) d x

y^{^{''}} + 2 y^{^{'}} + 2 y = sin (7 x)

\frac{\partial}{\partial x} (e^{- x^{3} - y^{6}})

\frac{d}{d x} (- x^{2} + y^{2} - 10)

\int sin^{3} (x) cos (y) d x