Question

(x^5 - 7x / x+1)' производная 

Answer 1

$y=frac{x^{5}-7x}{x+1}\ y'=(frac{x^{5}-7x}{x+1})'=(frac{u}{v})'=frac{u'v - uv'}{v^{2}}=frac{(x^{5}-7x)'(x+1)-(x^{5}-7x)(x+1)'}{(x+1)^{2}}=\ =frac{(5x^{4}-7)(x+1) - (x^{5}-7x)}{(x+1)^{2}}=frac{5x^{5}+5x^{4}-7x-7-x^{5}+7x}{(x+1)^{2}}=\ =frac{4x^{5}+5x^{4}-7}{x^{2}+2x+1}$