# Thread: derivatives using natural logs

1. ## derivatives using natural logs

y=6x^ln(x)

Before I take the derivative, is this right?

ln(y)=ln(x)[ln(6x)]

2. Originally Posted by yeloc
y=6x^ln(x)

Before I take the derivative, is this right?

ln(y)=ln(x)[ln(6x)]
No.

$\displaystyle \ln (y) = \ln \left( 6 x^{ln(x)} \right) = \ln (6) + \ln \left( x^{ln(x)} \right) = \ln (6) + \ln (x) \ln (x)$.

3. Ok that would explain it.

so the derivative would be:

y'=[(2ln(x))/x]*[6x^ln(x)] ?

4. Originally Posted by yeloc
Ok that would explain it.

so the derivative would be:

y'=[(2ln(x))/x]*[6x^ln(x)] ?
Yes.