Homework Soursefind the derivative by limit process of fxx23Solutionfx Lim
find the derivative by limit process of f(x)=x^(-2/3)
Solution
f\'(x) =Lim h--->0 [ f(x+h) - f(x)]/h
= [ (x+h)^-2/3 - x^-2/3 ]/h
take out x as common
= x^-2/3[(1+h/x)^-2/3 - 1]/h
= x^-2/3[ 1- 2h/3x -1]/h
= x-^2/3[-2h/3xh]
= x^-2/3[-2/3x]
= -2x^(-5/3)/3
= (-2/3)x^-5/3
![find the derivative by limit process of f(x)=x^(-2/3)Solutionf\'(x) =Lim h--->0 [ f(x+h) - f(x)]/h = [ (x+h)^-2/3 - x^-2/3 ]/h take out x as common = x^-2/3[](/WebImages/37/find-the-derivative-by-limit-process-of-fxx23solutionfx-lim-1110498-1761588715-0.webp "find the derivative by limit process of f(x)=x^(-2/3)Solutionf\'(x) =Lim h--->0 [ f(x+h) - f(x)]/h = [ (x+h)^-2/3 - x^-2/3 ]/h take out x as common = x^-2/3[")
