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

解答

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

(x^{2} + 1)^{3} + 6 x^{2} (x^{2} + 1)^{2}

求解步骤

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

使用微分乘法定则:

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

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

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

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

\frac{d}{d x} ((x^{2} + 1)^{3}) = 6 x (x^{2} + 1)^{2}

= 1 \cdot (x^{2} + 1)^{3} + 6 x (x^{2} + 1)^{2} x

化简

1 \cdot (x^{2} + 1)^{3} + 6 x (x^{2} + 1)^{2} x : (x^{2} + 1)^{3} + 6 x^{2} (x^{2} + 1)^{2}

= (x^{2} + 1)^{3} + 6 x^{2} (x^{2} + 1)^{2}

\frac{\partial}{\partial x} (8 x^{2} y + 5 x y^{3})

t an g e n t y = 7 x^{2} - 4 x, - 74

\int (x - 9)^{2} d x

\int_{0}^{\frac{π}{3}} tan^{5} (x) d x

y^{^{''}} + \frac{6}{x} y^{^{'}} + \frac{4}{x ^{2}} y = 0