Question

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

Answer 1

`(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)`