Calculus - Derivative of a Function

bobraymund
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Homework Statement



Find the derivative of the function.

Homework Equations



calcproblem.gif

The Attempt at a Solution


I have tried this out and came up with an answer that I'm not too confident with, I got:

calcsolution.gif


I would show my work on here, but don't know how to exactly, so my bad. Thanks in advance,
Bob
 
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That's what I got, and my calculator agrees.

Hint: e^u * e^-u = 1.
 
That's what I get too.
 
you can also note that x= tanh(u) and the derivative of tanh(u) is sech2(u).
 
Wow, thanks a lot for the prompt responses. Normally I'd post something like this on Yahoo Answers and not get an answer for a few days.

Again, thanks a bunch.

-Bob
 

Thread 'Prove that the integral is equal to ##\pi^2/8##'

Prove $$\int\limits_0^{\sqrt2/4}\frac{1}{\sqrt{x-x^2}}\arcsin\sqrt{\frac{(x-1)\left(x-1+x\sqrt{9-16x}\right)}{1-2x}} \, \mathrm dx = \frac{\pi^2}{8}.$$ Let $$I = \int\limits_0^{\sqrt 2 / 4}\frac{1}{\sqrt{x-x^2}}\arcsin\sqrt{\frac{(x-1)\left(x-1+x\sqrt{9-16x}\right)}{1-2x}} \, \mathrm dx. \tag{1}$$ The representation integral of ##\arcsin## is $$\arcsin u = \int\limits_{0}^{1} \frac{\mathrm dt}{\sqrt{1-t^2}}, \qquad 0 \leqslant u \leqslant 1.$$ Plugging identity above into ##(1)## with ##u...
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