`y = ln(ln(x^2))` Find the derivative of the function.

Friday, March 19, 2010

`y=ln(ln(x^2))`

To take the derivative of this, use the formula:

`(lnu)'=1/u*u'`

Applying the formula, the derivative of the function will be:

`y'=1/(ln (x^2)) * (ln (x^2))'`

`y'=1/(ln(x^2)) * 1/ x^2 * (x^2)'`

To take the derivative of the innermost function, apply the formula `(x^n)' = n*x^(n-1)` .

`y' = 1/(ln (x^2)) *1/x^2 * 2x`

`y'=2/(xln(x^2))`

Therefore, the derivative of the given function is `y' = 2/(xln(x^2))` .

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