Derivative of cot

A branch of mathematics, which represents the relationship among the angles and sides of a triangle, is said to be trigonometry. Different types of function are explained in the trigonometry; here we will discuss the different types of derivatives. Derivatives of trigonometric function are as follows:

⇨ d / da sin (a) = cos (a);

⇨ d / da cos (a) = - sin (a);

⇨ d / da tan (a) = sec2 (a);

⇨ d / ds csc (a) = - csc (a) cot (a);

⇨ d / da sec (a) = sec (a) tan (a);

⇨ d / da cot (a) = - csc2 (a);

These are all different types of derivatives of trigonometric functions. Here we will see the Derivative of cot a. Let’s discuss the prove of derivative of Cot a. First we write the cot a in the derivative form:

Proof = d / da cot a = - csc2 a; we can also write the cot a as:

⇨ Cot a = 1 / tan a;

We can also write in place of cot a as:

= d / da [1 / tan a]

We can solve it by u / v methods:

u / v = [u d / dx (v) – v d] / dx u / u2;                         

Put the expression in this method so that we can easily find the solution.

Now, we can write the above expression as:

= [tan a d / da (1) – 1 d / da tan a] / tan2 a;

 If we find the derivative of 1 and tan a, we get:

= [tan a (0) – 1 (sec2 a)] / tan2 a;

If we solve we get:

= [0 – sec2 a] / tan2 a;

On further solving we get:

= - csc2 a.

There are different types of methods to Solving Multistep Equations. To get more information about the multistep equation then prefer icse board syllabus and In the next session we will discuss about cosine law.