How do you find f'(x) using the definition of a derivative for f(x)=1/x^2?

1 Answer
Oct 15, 2015

f'(x) = -2/x^3

Explanation:

f(x) = 1/x^2
f'(x) = lim_(h \rarr 0) (f(x+h) - f(x))/h
= lim_(h \rarr 0) (1/(x+h)^2 - 1/x^2)/h
= lim_(h \rarr 0) (x^2 - (x+h)^2)/(h(x+h)^2x^2)
= lim_(h \rarr 0) (-2xh-h^2)/(h(x+h)^2x^2)
= lim_(h \rarr 0) (-2x-h)/((x+h)^2x^2)
= -2/x^3