This question may appear to be straightforward, but it is not. The reason is that the efficient numerical computation of p often depends on fast-converging series of the inverse tangent function. Ramanujan discovered many of these interesting series. But how does a person calculate a derivative? Let's look at an example. The nth derivative of arctan is 1/(1+x2).
What is the nth derivative of arctan?
The derivative of arctan(x) is 1/(1+x^2). You can find the proof of this by using the definition of derivatives. Alternatively, you can use trigonometric identities to simplify the expression. For instance, since tan(arctan(x)) = x, then you have that the derivative of tan(arctan(x)) is also 1/(1+x^2).
The arctan function is a differentiable function because it has a derivative at every point in its domain. An arctan function has a continuous curve, not a sharp corner. In other words, it is a function of x that is a power of two. In this case, 1/(1+x2) is the derivative of arctan.
The derivative of the inverse tangent function, also known as the arctangent function, is given by the following formula:
derivative of arctan(x) = 1/(1+x^2)
You can see that the derivative of the inverse tangent function is a simple fraction with a numerator of 1 and a denominator of (1+x^2). This should come as no surprise, since we know that the derivative of a fraction is simply the reciprocal of the square of the denominator.
Derivative of Arctan Formula
If you are wondering, "what is the derivative of arctan?", read on to find out. Basically, this derivative is a function that has an arctan coefficient. The derivative of arctan can be derived using trigonometric identities. The rule that you can use to find the derivative of arctan is arctan(x), where x is the arctan coefficient.
If you want to know more about how the arctan derivative works, consider its inverse: f'(x) = dfrac13. The inverse tangent function is the angle y in radians. Similarly, the arctan derivative of $f(x) = dfrac1sqrt3.
The derivative of arctan is similar to the derivative of arccot. They both have the same sign, but the negative sign makes the difference. This is because the function is not differentiable at every point of its domain. For example, if x is equal to -p/2, the derivative will be -p/2. So if x is p/2, arctan is p/2.