1. ## Differentiating

Hey guys the question asks to prove d/dt (Sin^-1(e^t)) = (e^-2t-1)^-1/2

I've got that the derivative is e^T/(1-e^2t)^1/2 but how do I get that to be the right hand side of the equation?

2. Originally Posted by Mathsnewbie
Hey guys the question asks to prove d/dt (Sin^-1(e^t)) = (e^-2t-1)^-1/2

I've got that the derivative is e^T/(1-e^2t)^1/2 but how do I get that to be the right hand side of the equation?
Multiply your last expression by $\displaystyle \frac{\displaystyle\frac{1}{\sqrt{e^{2t}}}}{\displ aystyle\frac{1}{\sqrt{e^{2t}}}}$

3. Can you explain to me how that works out? I multiply both the top and bottom by that but still don't get any furhter

4. Originally Posted by Mathsnewbie
Can you explain to me how that works out? I multiply both the top and bottom by that but still don't get any furhter
Use the chain rule on the left hand side to differentiate and get $\displaystyle \frac{e^t}{\sqrt{1 - e^{2t}}}$.

Now use Chop'S hint to show that the the right hand side is equal to this expression.

5. I think I must be multiplying it out wrong, I get when I multiply it out

((E^2t)^1/2).E^t/

(E^2t-(E^2t)^2)^1/2

From there I can't figure out a way to simplify further.