# How do you differentiate this with respect to s

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• June 1st 2010, 10:49 AM
adam_leeds
How do you differentiate this with respect to s
How do you differentiate the following with respect to s:

http://i47.tinypic.com/30js935.jpg

Thanks
• June 1st 2010, 11:26 AM
AllanCuz
Quote:

Originally Posted by adam_leeds
How do you differentiate the following with respect to s:

http://i47.tinypic.com/30js935.jpg

Thanks

Let $y = e^{ \lambda ( \frac{ p}{1-qs} - 1 ) }$

$lny = \lambda ( \frac{ p}{1-qs} - 1 )$

$lny = \lambda p (1-qs)^{-1} - \lambda$

Implicitly differentiate

$\frac{1}{y} y^{ \prime } = \lambda p (1-qs)^{-2} * q$

Resulting in

$y^{ \prime } = \lambda p q (1-qs)^{-2} ( e^{ \lambda ( \frac{ p}{1-qs} - 1 ) } )$