# [SOLVED] Derivative of a logarithmic function

• Nov 11th 2009, 07:39 AM
yzobel
[SOLVED] Derivative of a logarithmic function
I'm having trouble figuring out the derivative to this function:
f(t)=e^(2ln(t^3))

What I did:
f'(t)=e^(2ln(t^3)) x d/dt(2ln(t^3))
=e^(2ln(t^3)) x 6/t

Did I do this right? If I did is there any way I can simplify it more because it's not matching up to any of the answer choices I was given.
• Nov 11th 2009, 07:43 AM
tom@ballooncalculus
Simplify first...

f(t)=e^(2ln(t^3)) = (e^ln(t^3))^2 = ...?
• Nov 11th 2009, 07:56 AM
kjchauhan
$f(t)=e^{2\ln t^3}$

$\therefore f(t)=e^{\ln t^{3\times 2}}$

$\therefore f(t)= t^{6}$

$\therefore f'(t)=6 t^{5}$