How do you find the derivative of #ln(x^2-4)#?

1 Answer
Apr 13, 2016

# (2x)/(x^2 - 4)#

Explanation:

Using the #color(blue)" chain rule "#

#d/dx [ f(g(x)) ] = f'(g(x)) . g'(x) #

and the standard derivative # D(lnx) = 1/x #
#"------------------------------------------------------------------"#

f(g(x)) = #ln(x^2 - 4) rArr f'(g(x)) = 1/(x^2 - 4) #

and g(x) # = x^2 - 4 rArr g'(x) = 2x #
#"------------------------------------------------------------------"#

#rArr d/dx[f(g(x))] = 1/(x^2 - 4) xx 2x = (2x)/(x^2 - 4) #