Question

y = $( \frac{1}{x} +8)(5x-2)$
Найдите производную, плиз

Answer 1

f(x) = $\frac{1}{x} +8$
g(x) = 5x-2
f'(x) = $- \frac{1}{x^2}$
g'(x) = 5

(f(x)g(x))'= f'(x)g(x)+g'(x)f(x) 
(f(x)g(x))'=$- \frac{1}{x^2}$*(5x-2)+5*($\frac{1}{x}$+8) =
$\frac{2-5x}{x^2} + \frac{5}{x} +40 = \frac{2-5x+5x}{x^2} +40 = \frac{2}{x^2} +40$

Answer 2

y=(1/x +8)(5x-2)
y`=-1/x²(5x-2)+5*(1/x+8)=(2-5x)/x²+5(1/x+8)=(2-5x+5x+40x²)/x²=(40x²+2)/x²