# Thread: Derivatives: Solving for t -Xe^(-xt) + Ye^(-yt)

1. ## Derivatives: Solving for t -Xe^(-xt) + Ye^(-yt)

I have this equation and I know what the final answer should be but I am stuck on how to get to it using derivatives. Thanks in advance
Solving for t

-Xe-xt + Ye-yt

t= ln(y/x)(1/(y-x))

2. Originally Posted by mrooney
I have this equation and I know what the final answer should be but I am stuck on how to get to it using derivatives. Thanks in advance
Solving for t

-Xe-xt + Ye-yt

t= ln(y/x)(1/(y-x))
That is not an equation - there is no "equal to"(=) sign in there.

3. Originally Posted by Subhotosh Khan
That is not an equation - there is no "equal to"(=) sign in there.
sorry, its supposed to be equal to 0

4. Originally Posted by mrooney
sorry, its supposed to be equal to 0

Also, please explain how are X, x, Y & y are related.

5. Originally Posted by mrooney
I have this equation and I know what the final answer should be but I am stuck on how to get to it using derivatives. Thanks in advance
Solving for t

-Xe-xt + Ye-yt

t= ln(y/x)(1/(y-x))
Assuming x and X are meant to be the same thing (and that's a BIG assumption) and the same for the Y and y:

$-xe^{-xt} + ye^{-yt} =0$

$y*e^{-yt} = x* e^{-xt}$

$\frac {y}{x} = \frac {e^{-xt}}{e^{-yt}}$

$\frac{y}{x} = e^{yt-xt}$

Now take natural log of both sides and see if you can make t the subject.