Question

Найдите производную функции

Answer 1

$\boxed{y`=(\frac{x}{z})`=\frac{x`y-xy`}{y^2}}$

f`(x)=-x⁴+2x²-2x+1-2,5x⁻³;

$f`(x)=\frac{(2x^5+x^4-3x^2+5x+6)`3x^2-(2x^5+x^4-3x^2+5x+6)(3x^2)`}{9x^4}=\\\frac{(10x^4+4x^3-6x+5)3x^2-(2x^5+x^4-3x^2+5x+6)(6x)}{9x^4}=\\\frac{10x^5+4x^4-6x^2+5x-4x^5-2x^4+6x^2-10x-12}{3x^3}=\\\frac{6x^5+2x^4-5x-12}{3x^3};$

$g`(x)=\frac{1}{8t^5}-\frac{1}{2t^3}+\frac{1}{4t^2};$