Variant of inverse tangent derivative

In summary, the formula for the derivative of the inverse tangent function is 1/(1+x^2). It is related to the derivative of the tangent function as its reciprocal. The derivative can be simplified to 1/(1+x^2) or (1-cosx)/sin^2x. It can be positive or negative depending on the value of x and is used in physics and engineering to calculate rates of change of angles in rotational motion problems.
  • #1
Saterial
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Homework Statement


1/(u^2+4)


Homework Equations





The Attempt at a Solution



I know that 1/(x^2+1) is the derivative of the inverse tangent function, and that is proved by using tany = x, derivative of both sides with secx=(1+tan^2x) and tan^2x = x^2.

I don't know how to use the proof of the inverse tangent derivative to calculate the integral of 1/(u^2+4). Am I approaching this in an incorrect way?
 
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  • #2
Think about how you can turn that 4 into a 1 without changing the value of the whole expression.
 

1. What is the formula for the derivative of the inverse tangent function?

The formula for the derivative of the inverse tangent function is 1/(1+x^2).

2. How is the derivative of the inverse tangent function related to the derivative of the tangent function?

The derivative of the inverse tangent function is the reciprocal of the derivative of the tangent function.

3. Can the derivative of the inverse tangent function be simplified?

Yes, the derivative of the inverse tangent function can be simplified to 1/(1+x^2) or (1-cosx)/sin^2x.

4. Is the derivative of the inverse tangent function always positive?

No, the derivative of the inverse tangent function can be positive or negative depending on the value of x.

5. How can the derivative of the inverse tangent function be used in real-world applications?

The derivative of the inverse tangent function is used in physics and engineering to calculate the rate of change of an angle with respect to time, such as in rotational motion problems.

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