If f(x)=1/x^2. find f'(x). f'(x)= lim h->0 (f(x+h)-f(x))/h

Question

Must use the limit definition of derivatives to find the derivative

Answer 1

lim {[1/(x+h)²] - (1/x)}/h is the derivative when h-->0

Forget the lim for the moment

(1/h)[x² - (x+h)²]/[x²((x+h)²]=(-2x-h)/[x²(x+h)²]...note the h divided out of the numerator

When h -->0 the numerator goes to -2x and the denominator to x⁴

and the limit is -2/x³