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

解答

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

5 x^{4} + 4 x^{3} + 3 x^{2} + 4 x

求解步骤

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

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

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

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

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

化简

2 x (x^{3} + x^{2} + 1) + (3 x^{2} + 2 x) (x^{2} + 1) : 5 x^{4} + 4 x^{3} + 3 x^{2} + 4 x

= 5 x^{4} + 4 x^{3} + 3 x^{2} + 4 x

\frac{\partial}{\partial x} (e^{6 x})

x \to 0 - lim (\frac{0}{x})

\frac{\partial}{\partial x} (y^{4} e^{- x})

\int x^{2} (x^{3} - 2)^{4} d x

\int \frac{( ln ( x ^{5} ) )}{x} d x