Question

Найдите производные функций:
а) $y= frac{1+2x}{3-5x}$
b) $y= frac{ x^{2} }{2x-1}$
c) $y= frac{3x-2}{5x+8}$
d) $y= frac{3-4x}{ x^{2} }$

Answer 1

$( frac{1+2x}{3-5x})'= frac{(1+2x)'(3-5x)-(1+2x)(3-5x)'}{(3-5x)^2}= frac{6-10x+5+10x}{(3-5x)^2}= frac{11}{(3-5x)^2}=$$frac{11}{25x^2-30x+9}$

$(frac{x^2}{2x-1})'= frac{4x^2-2x-2x^2}{(2x-1)^2}= frac{2x^2-2x}{(2x-1)^2}= frac{2x(x-1)}{(2x-1)^2}$

$( frac{3x-2}{5x+8})'= frac{15x+24-15x+10}{(5x+8)^2}= frac{34}{(5x+8)^2}= frac{34}{25x^2+80x+64}$

$( frac{3-4x}{x^2})'= frac{-4x^2-6x+8x^2}{x^4}= frac{4x^2-6x}{x^4}= frac{2x(2x-3)}{x^4}= frac{4x-6}{x^3}$