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

解答

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

15 (5 x - 1)^{2} (x^{2} + 1)^{5} + 10 x (x^{2} + 1)^{4} (5 x - 1)^{3}

求解步骤

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

使用微分乘法定则:

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

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

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

\frac{d}{d x} ((5 x - 1)^{3}) = 15 (5 x - 1)^{2}

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

= 15 (5 x - 1)^{2} (x^{2} + 1)^{5} + 10 x (x^{2} + 1)^{4} (5 x - 1)^{3}

t an g e n t f (x) = 8 - 2 x^{2}, at x = 0

\int x 2 x + 5 d x

s l o p e f (x) = 25 x^{\frac{4}{5}}

n = 1 \sum \infty (- 5)^{n} x^{n}

\frac{d}{d t} (\frac{3 t}{t - 9})