Differentiation Problem

Feb 2010
76
2
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
Feb 2009
2,763
1,146
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 \(\displaystyle te^{-\alpha t}\)
 
Jan 2010
354
173
\(\displaystyle q=\frac{1}{\alpha^2}-\left(\frac{t}{\alpha}+\frac{1}{\alpha^2}\right)e^{-\alpha t}\)

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

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

\(\displaystyle = t e^{-\alpha t}\)