How do you find the derivative of g(x) = −2/(x + 1)g(x)=2x+1 using the limit definition?

1 Answer
Aug 13, 2016

=2/(x+1)^2=2(x+1)2

Explanation:

f'(x) = lim_(hrarr0) (f(x+h)-f(x))/h

=lim_(hrarr0) (-2/(x+h+1) + 2/(x+1))/h

=lim_(hrarr0)((-2(x+1))/((x+h+1)(x+1)) + (2(x+h+1))/((x+h+1)(x+1)))/h

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

=2/(x+1)^2