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

1 Answer

Aug 13, 2016

#=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#

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