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

解答

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

4 x^{3}

求解步骤

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

使用微分乘法定则:

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

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

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

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

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

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

化简

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

= 4 x^{3}

\int t sec^{2} (2 t) d t

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

\frac{\partial}{\partial x} (e^{- 2 t} cos (π x))

\frac{d y}{d t} = \frac{t}{y e ^{y + t^{2}}}

\int \frac{x ^{2}}{a ^{2} + ( x - b ) ^{2}} d x