# Math Help - Derivative of a (very) simple log function

1. ## Derivative of a (very) simple log function

$y = (ln x)^4$

The given answer is $4/x (ln x)^3$. The problem I'm having is, isn't it one of the rules that an exponent is transferred to the base? I mean, should $(ln x)^4$ become $4 (ln x)$? The answer used the chain rule right away without modifying the function.

2. Originally Posted by Archduke01
$y = (ln x)^4$

I mean, should $(ln x)^4$ become $4 (ln x)$?
No. $ln(x^4) = 4\ln(x)$

This is different from $(\ln(x))^4$. For ln(x^4) the power only applies to 'x' whilst your question concerns the whole term ln(x) raised to the 4th power.