derivative of e^6e^x?

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- Feb 10th 2010, 05:55 PMBugzLooneyFirst and second derivative of e^6e^x?
derivative of e^6e^x?

- Feb 10th 2010, 05:56 PMGeneral
- Feb 10th 2010, 07:14 PMBugzLooney
Yes that is the question indeed.

- Feb 10th 2010, 07:20 PMdanielomalmsteen
The first derivate, using the chain rule

$\displaystyle f(x)=e^{6e^x}$

$\displaystyle f'(x)=e^{6e^x} \cdot (6e^x)'$

$\displaystyle f'(x)=6e^{6e^x} \cdot (e^x)'$

$\displaystyle f'(x)=6e^{6e^x+x}$ - Feb 10th 2010, 07:22 PMPulock2009
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, 07:23 PMPulock2009
for the second derivative differetiate again as you already might be knowing!

- Feb 10th 2010, 07:23 PMdanielomalmsteen
The second derivate

$\displaystyle f'(x)=6e^{6e^x+x}$

$\displaystyle f''(x)=6e^{6e^x+x} \cdot (6e^x+x)'$

$\displaystyle f''(x)=6e^{6e^x+x} \cdot (6e^x+1)$ - Feb 10th 2010, 07:54 PMGeneral