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

1 Answer
Jun 28, 2016

f'(x)=2x+1

Explanation:

lim_(hrarr0)[[(x+h)^2+x+h]-[x^2+x]]/h

lim_(hrarr0)[[x^2+2xh+h^2+x+h]-[x^2+x]]/h

lim_(hrarr0)[x^2+2xh+h^2+x+h-x^2-x]/h

lim_(hrarr0)[2xh+h^2+h]/h

lim_(hrarr0)[h(2x+h+1)]/h

lim_(hrarr0)2x+h+1=2x+0+1=2x+1