How do you differentiate the following with respect to s:

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

Thanks

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- Jun 1st 2010, 10:49 AMadam_leedsHow 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 - Jun 1st 2010, 11:26 AMAllanCuz
Let $\displaystyle y = e^{ \lambda ( \frac{ p}{1-qs} - 1 ) } $

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

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

Implicitly differentiate

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

Resulting in

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