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Derivative of tan -1 x?

TopA 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 + x2;
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 + x2;
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 ⊖) sec2 ⊖= 1;
We can write it as:
= f’ (tan ⊖) = 1 / sec2 ⊖…… (1);
We can write the sec2 ⊖ as:
Sec2 ⊖ = tan2 ⊖ + 1;
Now assume x = tan ⊖ then we can write it as:
→ sec2 ⊖ = 1 + x2……… (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 / sec2 ⊖…… (1);
= f’ (tan ⊖) = 1 / 1 + x2;
So we write the derivative of tan inverse x is:
= d / dx tan-1 x = 1 / 1 + x2;
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.