derivative (3x-1)^7(2x+1)^5

解答

导数

(3 x - 1)^{7} (2 x + 1)^{5}

21 (3 x - 1)^{6} (2 x + 1)^{5} + 10 (2 x + 1)^{4} (3 x - 1)^{7}

求解步骤

\frac{d}{d x} ((3 x - 1)^{7} (2 x + 1)^{5})

使用微分乘法定则:

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

f = (3 x - 1)^{7}, g = (2 x + 1)^{5}

= \frac{d}{d x} ((3 x - 1)^{7}) (2 x + 1)^{5} + \frac{d}{d x} ((2 x + 1)^{5}) (3 x - 1)^{7}

\frac{d}{d x} ((3 x - 1)^{7}) = 21 (3 x - 1)^{6}

\frac{d}{d x} ((2 x + 1)^{5}) = 10 (2 x + 1)^{4}

= 21 (3 x - 1)^{6} (2 x + 1)^{5} + 10 (2 x + 1)^{4} (3 x - 1)^{7}

\frac{d}{d y} (e^{2 y})

d er i v a t i v e f (x) = x^{6} (x - 1)^{5}

\int (x^{4} - \frac{1}{2} x^{3} + \frac{1}{4} x - 2) d x

n = 1 \sum \infty (\frac{4 π}{5})^{n}

\int x^{2} + x - 3 d x