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

解答

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

2 (1 - 3 x^{2} y^{2})

求解步骤

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

将

y

视为常数

将常数提出:

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

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

使用微分乘法定则:

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

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

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

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

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

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

化简

2 (1 \cdot (1 - x^{2} y^{2}) + (- 2 y^{2} x) x) : 2 (1 - 3 x^{2} y^{2})

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

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

\frac{d}{d x} (x^{3} - 100 x + 1)

\frac{d ^{2}}{d x ^{2}} (e^{7 x - 4})

\int arctan (2 t) d t

d er i v a t i v e f (x) = x^{4} - 8 x^{3}