1. Differentiation Problem

I have an engineering application, that amounts to a differentiation problem that has me stumped.

If $\displaystyle q=\frac{1}{\alpha^2}-(\frac{t}{\alpha}+\frac{1}{\alpha^2})e^{-\alpha t}$

Find $\displaystyle \frac{dq}{dt}$.

I came up with $\displaystyle -\frac{t}{e^{\alpha t}}$ and several other versions, but I know that I'm off.

Can anyone put me on track?

2. Originally Posted by kaiser0792
I have an engineering application, that amounts to a differentiation problem that has me stumped.

If $\displaystyle q=\frac{1}{\alpha^2}-(\frac{t}{\alpha}+\frac{1}{\alpha^2})e^{-\alpha t}$

Find $\displaystyle \frac{dq}{dt}$.

I came up with $\displaystyle -\frac{t}{e^{\alpha t}}$ and several other versions, but I know that I'm off.

Can anyone put me on track?

I get $\displaystyle te^{-\alpha t}$

3. $\displaystyle q=\frac{1}{\alpha^2}-\left(\frac{t}{\alpha}+\frac{1}{\alpha^2}\right)e^ {-\alpha t}$

$\displaystyle \frac{dq}{dt} = -\left(\frac{t}{\alpha}+\frac{1}{\alpha^2}\right) \left( -\alpha e^{-\alpha t} \right) - \frac{1}{\alpha} e^{-\alpha t}$

$\displaystyle = t e^{-\alpha t} + \frac{1}{\alpha} e^{-\alpha t} - \frac{1}{\alpha} e^{-\alpha t}$

$\displaystyle = t e^{-\alpha t}$