Help on inverse trig differentiation

In summary, the conversation was about a problem in a calculus textbook where the derivative of y = Arctan(x^2-1) + Arccscx, x > 1, was supposed to be zero according to the answer on the back, but the person could not solve it. The other person in the conversation pointed out that the answer should be zero because \tan^{-1} \sqrt{x^2-1} + \csc^{-1}x = \frac {\pi}{2}, and the first person realizes their mistake.
  • #1
Simfish
Gold Member
823
2
Hi, I kow about the chain rule and such; but there I cannot solve a problem in my calc textbook.

y = Arctan(x^2-1) + Arccscx, x > 1.

Answer on back says 0; but my answer didn't go to 0. BTW, this is just one problem from a HW assignment so this shouldn't count as cheating.

Thanks!

-Simfish
 
Last edited:
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  • #2
The derivative should be zero because

[tex]\tan^{-1} \sqrt{x^2-1} + \csc^{-1}x = \frac {\pi}{2}[/tex]
 
  • #3
Sleazy Tide!
Why didn't I see that..:grumpy:
 
  • #4
arildno said:
Sleazy Tide!
Why didn't I see that..:grumpy:

LoL! Oh, you would have seen it - I just happened to see it first.
 

1. What is inverse trig differentiation?

Inverse trig differentiation is a mathematical process used to find the derivative of a function that involves inverse trigonometric functions such as sin-1, cos-1, and tan-1.

2. Why is inverse trig differentiation important?

Inverse trig differentiation is important because it allows us to find the rate of change of a function involving inverse trigonometric functions. This is useful in many fields such as physics, engineering, and economics.

3. How is inverse trig differentiation different from regular differentiation?

Inverse trig differentiation involves differentiating inverse trigonometric functions, which have unique rules and formulas. Regular differentiation deals with differentiating standard algebraic functions.

4. What are some common inverse trig differentiation formulas?

Some common inverse trig differentiation formulas include:
- d/dx(sin-1x) = 1/√(1-x2)
- d/dx(cos-1x) = -1/√(1-x2)
- d/dx(tan-1x) = 1/(1+x2)

5. How can I improve my skills in inverse trig differentiation?

The best way to improve your skills in inverse trig differentiation is through practice and understanding the underlying concepts. You can also seek help from textbooks, online resources, or a tutor if needed.

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