# Derivative involving inverse trigonometric functions

1. Mar 7, 2012

### biochem850

1. The problem statement, all variables and given/known data
Find the derivative of:
sqrt(x^2-4)-2tan^-1{.5*sqrt(x^2-4)}

2. Relevant equations
U'/1+U^2
U'=x/2sqrt(x^2-4)
1+U^2=x^2

3. The attempt at a solution

I combined the above components but my answer is incorrect. I feel that I might have the wrong answer for "1+U^2". I just cannot seem to catch my error at the moment.
1. The problem statement, all variables and given/known data

2. Relevant equations

3. The attempt at a solution

2. Mar 8, 2012

### ehild

Did you mean the following function?

$$\sqrt{(x^2-4)}-2\arctan\left(0.5 \sqrt{(x^2-4)}\right)$$

What do you mean on U'/1+U^2? Are no parentheses missing?

Did you mean the derivative of arctan(U)?

$$\frac{U'}{1+U^2}$$

with $$U=0.5\sqrt{(x^2-4)}$$
and
$$U'=0.5 \frac{x}{\sqrt{(x^2-4)}}$$?

Recalculate U^2+1. It is not x^2.

ehild

Last edited: Mar 8, 2012
3. Mar 8, 2012

### biochem850

My U'=$\frac{x}{2\sqrt{x^2-4}}$

When I square $\frac{\sqrt{x^2-4}}{2}$ and add one the only other answer I get is $\frac{x^2}{4}$
I've been working for a while and perhaps I'm missing something very simple.

Last edited: Mar 8, 2012
4. Mar 8, 2012

### biochem850

$\frac{\sqrt{x^2-4}}{x}$
I made a simple mistake in calculating 1+U$^{2}$