How do you differentiate the following with respect to s:
Thanks
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 ) } ) $