Question

Помогите 465 пожалуйста

Answer 1

$1); ; y=(x^3-2x^2+3)^{17}\\y'=17(x^3-2x^2+3)^{16}cdot (x^3-2x^2+3)'=17(x63-2x^2+3)^{16}cdot (3x^2-4x)\\\2); ; y=sqrt{1-x^4}+frac{1}{x^2+3}\\y'=frac{1}{2sqrt{1-x^2}cdot}(1-x^4)'+frac{-(x^2+3)'}{(x^2+3)^2}=frac{1}{2sqrt{1-x^4}}cdot (-4x^3)-frac{2x}{(x^2+3)^2}=\\=-frac{2x^3}{sqrt{1-x^4}}-frac{2x}{(x^2+3)^2}\\\3); ; y=sqrt{4x^2+5}; ; ,; ; ; (sqrt{u})'=frac{1}{2sqrt{u}}cdot u'; ; ,; ; u=4x^2+5\\y'=frac{1}{2sqrt{4x^2+5}}cdot (4x^2+5)'=frac{1}{2sqrt{4x^2+5}}cdot 8x=frac{4x}{sqrt{4x^2+5}}$

$4); ; y=(3-x^3)^5+sqrt{2x^2+3}\\y'=5(3-x^3)^4cdot (3-x^3)'+frac{1}{2sqrt{2x^2+3}}cdot (2x^2+3)'=\\=5(3-x^3)^4cdot (-3x^2)+frac{1}{2sqrt{2x^2+3}}cdot 4x=-15x^2cdot (3-x^3)^4+frac{2x}{sqrt{2x^2+3}}$