Inverse Trig function derivative

In summary, inverse trigonometric functions are mathematical functions that perform the opposite operation of a regular trigonometric function. The six inverse trigonometric functions are arc sine, arc cosine, arc tangent, arc cotangent, arc secant, and arc cosecant. The derivative of an inverse trigonometric function can be found using the chain rule. The derivative of inverse sine (sin⁻¹x) is equal to 1/√(1-x²). Finding the derivative of an inverse trigonometric function has practical applications in solving real-world problems and in advanced mathematical concepts such as calculus.
  • #1
EvilBunny
39
0

Homework Statement



Let

arctan ([tex]\sqrt{3x^2 -1}[/tex])


then dy/dx


Well I know that the derivative of arctanx is

1/ 1 + x ² but when I got something other then simply x I don't know how to proceed
 
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  • #2
x=the radical

example

[tex]y=\arctan{(x^2)}[/tex]

[tex]y'=\frac{2x}{1+(x^2)^2}[/tex]
 
  • #3
Neat I get it, thanks.
 

1. What are inverse trigonometric functions?

Inverse trigonometric functions are mathematical functions that perform the opposite operation of a regular trigonometric function. They are used to find the angle or side length of a right triangle when given the ratio of its sides.

2. What are the six inverse trigonometric functions?

The six inverse trigonometric functions are arc sine (sin⁻¹), arc cosine (cos⁻¹), arc tangent (tan⁻¹), arc cotangent (cot⁻¹), arc secant (sec⁻¹), and arc cosecant (csc⁻¹).

3. How do you find the derivative of an inverse trigonometric function?

The derivative of an inverse trigonometric function can be found using the chain rule, where the derivative of the inverse function is multiplied by the derivative of the original function.

4. What is the derivative of inverse sine?

The derivative of inverse sine (sin⁻¹x) is equal to 1/√(1-x²).

5. What is the purpose of finding the derivative of an inverse trigonometric function?

Finding the derivative of an inverse trigonometric function can be useful in solving real-world problems involving angles or triangles, as well as in calculus and other advanced mathematical concepts.

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