# Differentiation Problem

#### 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?

#### matheagle

MHF Hall of Honor
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 $$\displaystyle te^{-\alpha t}$$

#### drumist

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

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

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

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