# First and second derivative of e^6e^x?

• Feb 10th 2010, 06:55 PM
BugzLooney
First and second derivative of e^6e^x?
derivative of e^6e^x?
• Feb 10th 2010, 06:56 PM
General
Quote:

Originally Posted by BugzLooney
derivative of e^6e^x?

Is it $e^{6e^x}$ ?
• Feb 10th 2010, 08:14 PM
BugzLooney
Yes that is the question indeed.
• Feb 10th 2010, 08:20 PM
danielomalmsteen
The first derivate, using the chain rule

$f(x)=e^{6e^x}$
$f'(x)=e^{6e^x} \cdot (6e^x)'$
$f'(x)=6e^{6e^x} \cdot (e^x)'$
$f'(x)=6e^{6e^x+x}$
• Feb 10th 2010, 08:22 PM
Pulock2009
consider the expression equal to say t. take logs on both sides of the equation then differentiate and u should get the derivative of t ie. the derivative of your expression.
• Feb 10th 2010, 08:23 PM
Pulock2009
for the second derivative differetiate again as you already might be knowing!
• Feb 10th 2010, 08:23 PM
danielomalmsteen
The second derivate

$f'(x)=6e^{6e^x+x}$
$f''(x)=6e^{6e^x+x} \cdot (6e^x+x)'$
$f''(x)=6e^{6e^x+x} \cdot (6e^x+1)$
• Feb 10th 2010, 08:54 PM
General
Quote:

Originally Posted by BugzLooney
Yes that is the question indeed.

If $g$ is a differentiable function and $f(x)=e^{g(x)}$, then $f$ is differentiable and:
$f'(x)=e^{g(x)} g'(x)$.
Just apply this on your problem.