What is the derivative of #f(x) = ln(x^2+3x-5)#?

1 Answer
KillerBunny
Nov 7, 2015

#(2x+3)/(x^2+3x-5)#

Explanation:

The derivative of a logarithm is the inverse of the argument. Since the argument is a function itself, we need to use the rule for deriving composite functions, which means that we have to multiply by the derivative of the argument, too:

#d/dx f(g(x)) = f'(g(x)) * g'(x)#

So, since #f'(g(x)) = 1/(x^2+3x-5)#, we need to find the derivative of # x^2+3x-5#, which is #2x+3#. So, the whole derivative is

# 1/(x^2+3x-5)*2x+3 = (2x+3)/(x^2+3x-5)#

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