**A branch of mathematics which deals in angles and sides of a triangle and also show the relationship between the angles and sides of a triangle are known as Trigonometry.**There are so many types of Functions come under trigonometry. Now we will see the Derivative of Tan Inverse X. As we know that Derivative of Tan Inverse X is 1 / 1 + x

^{2};

Let’s see the proof of Derivative of Tan Inverse X.

First we write the tan

^{-1}x in the derivative form:

Proof = d / dx tan

^{-1}x = 1 / 1 + x

^{2};

Now we have to assume the function for finding the Derivative of Tan Inverse X.

Let the function f (x) = tan

^{-1}x,

If we put the value of x = tan ⊖;

On putting the value we get:

= f (tan ⊖) = ⊖;

If we differentiate it then we get:

= f’ (tan ⊖) sec

^{2}⊖= 1;

We can write it as:

= f’ (tan ⊖) = 1 / sec

^{2}⊖…… (1);

We can write the sec

^{2}⊖ as:

Sec

^{2}⊖ = tan

^{2}⊖ + 1;

Now assume x = tan ⊖ then we can write it as:

→ sec

^{2}⊖ = 1 + x

^{2………}(2);

So put the value of equation (2) in the equation (1);

On putting the value in the equation 1 we get:

= f’ (tan ⊖) = 1 / sec

^{2}⊖…… (1);

= f’ (tan ⊖) = 1 / 1 + x

^{2};

So we write the derivative of tan inverse x is:

= d / dx tan

^{-1}x = 1 / 1 + x

^{2};

One condition is given for this inverse derivative function which is shown below:

When we put the limit of x is

__+__∞ then we get the value of derivative of tan inverse x is 0.

= d / dx tan

^{-1}x = 0;

This is how we can prove the Derivative Of tan inverse X.