# Derivative of cotangent

The derivative of the cotangent of a function f (x) is equal to the cosecant of said squared function, multiplied by the derivative of f (x), and also multiplied by -1.

Likewise, the cosecant can be replaced by one between the squared sine of the same function, so we would have the following equivalence:

At this point, it is important to specify that the derivative of a function is calculated, in mathematical terms, with the following formula:

We must remember that the derivative is a mathematical function that allows us to calculate the rate of change of a (dependent) variable. This, when a variation is registered in another variable (which would be the independent one) that affects it.

Another concept that we will need is that of cotangent, which is a trigonometric function applied to a right triangle. Thus, the cotangent of an angle is equal to the ratio of the adjacent leg to the opposite leg.

A right triangle is made up of one side called the hypotenuse, which is in front of the right angle (90º), while the other two smaller sides, opposite the acute angles, are called the legs.

## Examples of derivative of cotangent

To better understand what has been explained, let's see some examples:

Now let's see an example with a quadratic equation:

Finally, let's look at an example of a squared cotangent: