derivative y=(x+1)^2(x^2+2x)

解答

导数

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

4 x^{3} + 12 x^{2} + 10 x + 2

求解步骤

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

使用微分乘法定则:

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

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

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

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

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

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

化简

2 (x + 1) (x^{2} + 2 x) + (2 x + 2) (x + 1)^{2} : 4 x^{3} + 12 x^{2} + 10 x + 2

= 4 x^{3} + 12 x^{2} + 10 x + 2

d er i v a t i v e \frac{tan ( x )}{2}

d er i v a t i v e \frac{x ^{\frac{1}{2}} - 1}{x ^{\frac{1}{2}}}

d er i v a t i v e 1 + ln (x)

d er i v a t i v e 7 x^{5} + 17

d er i v a t i v e x^{3} - 3 x - 5