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Derivatives of Inverse?

TopIn trigonometric we will study the relationship among angles and sides of a triangle. In the trigonometric there are different types of function. Let’s see the different types of Derivatives Of Inverse in the trigonometric Functions:
= d / da sin (a) = cos (a);
= d / da cos (a) = - sin (a);
= d / da tan (a) = sec2 (a);
= d / da csc (a) = - csc (a) cot (a);
= d / da sec (a) = sec (a) tan (a);
= d / da cot (a) = - csc2 (a);
These are different types of derivatives of inverse of trigonometric Functions.
Now we will see how to find the derivatives of inverse with the help of an example:
Suppose a function is given f (p) = p2 sin (4x); then we have to find the inverse derivative of a given function.
We have to use the product and Chain Rule for finding the inverse of trigonometric functions.
Here UV method is used which is given as u.v = u d/ dx v + v. d / dx u;
Here the given function is:
f (p) = p2 sin (4p);
Now we use uv method for finding the derivative this given Inverse Function. We can write as:
f (p) = d / dp p2 .sin (4p) +p2 d / dx (sin (4p));
If we differentiate the value p2then we get 2p and we differentiate sin 4p then we get 4 cos 4p;
Now putting these values in the given function we get:
f (p) = 2p.sin (4p) +p2 . 4(cos (4p));
We can also write it as:
f (p) = 2p.sin (4p) + 4p2 4(cos (4p));
This is how you can calculate the inverse derivatives of trigonometric function.