Question

знайдіть похідну пожалуйста
а) y=2x^3
б) y=1:x^6
в) y=x+1:x-1

Answer 1

$1. [u+v]'=u'+v'\\ 2. [x^a]'=a*x^{a-1}\\ 3. [C*f(x)]'=C*[f(x)]'=C*f'(x)\\4. [C]'=0$

$1. y'(x)=[2x^3]'=2*[x^3]'=2*3*x^{3-1}=6x^2\\ 2. y'(x)=[1:x^6]'=[frac{1}{x^6}]'=[x^{-6}]'=-6*x^{-6-1}=\\=-6*x^{-7}=-6*frac{1}{x^7}=-frac{6}{x^7}\\ 3. y'(x)=[x+1:x+1]'=[x+frac{1}{x}+1]'=[x^1+x^{-1}+1]=\\ =[x^1]'+[x^{-1}]'+[1]'=1*x^{1-1}+(-1)*x^{-1-1}+0=\\ =1*x^0-x^{-2}=1*1-frac{1}{x^2}=1-frac{1}{x^2}$