Derivative involving inverse trigonometric functions

In summary, the conversation involved finding the derivative of a function and discussing potential errors and solutions. The final answer was \frac{\sqrt{x^2-4}}{x}.
  • #1
biochem850
51
0

Homework Statement


Find the derivative of:
sqrt(x^2-4)-2tan^-1{.5*sqrt(x^2-4)}




Homework Equations


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


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.
 
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  • #2
Did you mean the following function? [tex]\sqrt{(x^2-4)}-2\arctan\left(0.5 \sqrt{(x^2-4)}\right)[/tex]

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

Did you mean the derivative of arctan(U)?

[tex]\frac{U'}{1+U^2}[/tex]

with [tex]U=0.5\sqrt{(x^2-4)}[/tex]
and
[tex]U'=0.5 \frac{x}{\sqrt{(x^2-4)}}[/tex]?Recalculate U^2+1. It is not x^2.

ehild
 
Last edited:
  • #3
My U'=[itex]\frac{x}{2\sqrt{x^2-4}}[/itex]

When I square [itex]\frac{\sqrt{x^2-4}}{2}[/itex] and add one the only other answer I get is [itex]\frac{x^2}{4}[/itex]
I've been working for a while and perhaps I'm missing something very simple.
 
Last edited:
  • #4
I've gotten the answer:

[itex]\frac{\sqrt{x^2-4}}{x}[/itex]

I made a simple mistake in calculating 1+U[itex]^{2}[/itex]

Thanks for the help!
 

1. What is the general formula for finding the derivative of inverse trigonometric functions?

The general formula for finding the derivative of inverse trigonometric functions is d/dx [f^-1(x)] = 1 / (f'(f^-1(x))), where f(x) is the inverse trigonometric function and f'(x) is the derivative of the function f(x).

2. How do I find the derivative of arcsin?

To find the derivative of arcsin, you can use the general formula d/dx [arcsin(x)] = 1 / sqrt(1 - x^2). This can also be written as d/dx [sin^-1(x)] = 1 / sqrt(1 - x^2).

3. Can I use the power rule to find the derivative of inverse trigonometric functions?

No, the power rule cannot be used to find the derivative of inverse trigonometric functions. You must use the general formula d/dx [f^-1(x)] = 1 / (f'(f^-1(x))).

4. How do I find the derivative of arctan?

To find the derivative of arctan, you can use the general formula d/dx [arctan(x)] = 1 / (1 + x^2). This can also be written as d/dx [tan^-1(x)] = 1 / (1 + x^2).

5. Are there any special rules for finding the derivative of inverse trigonometric functions?

Yes, there are a few special rules for finding the derivative of inverse trigonometric functions. These include the general formula and specific formulas for arcsin and arctan. It is important to remember these formulas and to use them correctly when finding the derivative of inverse trigonometric functions.

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