arctan

In the previous post we have discussed about arcsin and In today's session we are going to discuss about arctan. Hi friends in mathematics we will study different types of trigonometric functions. Here we will discuss one of the trigonometric function that is arctan. Before learn the concept of arc tan first we will discuss about trigonometry. Trigonometry can be defined as a branch of mathematics which is used to show the relationship among the angles and sides of triangle. 

Now we will discuss inverse tangent function of arc tan. The inverse of arc tan is given as:

=> arc tan p = 2 arc tan p / 1 + √ (1 + p²);

The derivative of tan inverse ‘p’ is 1 / 1 + p²;

Let’s see the proof of derivative tan inverse ‘p’.

First write the tan^-1 p in the derivative form:

=> d / dp tan^-1 p = 1 / 1 + p²;

Now, assume that the function for finding derivative tan inverse ‘p’.

Let function f (p) = tan^-1 p,

If we put the value of p = tan ⊖;

On putting the value we get:

= f (tan ⊖) = ⊖;

If we differentiate it then, we get:

= f’ (tan ⊖) sec² ⊖= 1;

We can rewrite it as:

= f’ (tan ⊖) = 1 / sec² ⊖…… (1);

We can write the sec² ⊖ as:

Sec² ⊖= tan² ⊖ + 1;

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

→ sec² ⊖= 1 + q²……… (2);

After this, put the value of equation (2) in the equation (1);

On putting the value in equation 1 we get:

= f’ (tan ⊖) = 1 / sec² ⊖…… (1);

= f’ (tan ⊖) = 1 / 1 + p²;

Now, we can write the derivative of tan inverse p as:

= d / dp tan^-1 p = 1 / 1 + p²;

One condition is given for this inverse derivative function as:

When we put the limit of p is +∞ then we get the value of derivative of tan inverse p is 0. (know more about arctan, here)   

= d / dp tan^-1 p = 0;  

This is how we proved derivative of tan inverse 'p'. Tangential Acceleration is a rate in which the velocity of a body change with time. The cbse syllabus for class 9th 2013 is necessary for 9^th class student.