I have mathematical question.
in this image, why left side of above equation is equal with left side of below equation?
can you explain in detail expression..?
Deriving $[\dot P^e(\tau)+\lambda P^e(\tau)]e^{\lambda\tau} = \frac{d}{d\tau} P^e(\tau)e^{\lambda\tau}$
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derivatives
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0Seems quite off-topic to me. I've voted for migration. By the way, the title is useless in any forum but especially in a mathematical forum: please replace it by something more specific. What's AEH and why is anyone who knows about ordinary differential equations expected to know what it means? – 2017-01-18
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0No need to know; all you need to do is see that it's an application of the product rule. – 2017-01-18
1 Answers
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Did you try it differentiating back to see the result.
This is a simple extension of $\frac{d}{dt}(xy) = x \frac{dy}{dt} + y \frac{dx}{dt}$
$ \frac{d}{d \tau} P_{e}(\tau)e^{\lambda t} \implies$ $\dot P_{e}(\tau)e^{\lambda \tau}$ + $P_{e}(\tau) \frac{d}{d \tau}e^{\lambda \tau} \implies $ $\dot P_{e}(\tau)e^{\lambda t}$ + $\lambda P_{e}(\tau)e^{\lambda \tau}$ $\implies$ $e^{\lambda \tau}(\dot P_{e}(\tau) + \lambda P_{e}(\tau))$