## Derivative of Cot

### The derivative of the cotangent function (Cot) can be found using the quotient rule

The derivative of the cotangent function (Cot) can be found using the quotient rule.

Let’s consider the cotangent function as the ratio of the cosine function (cos) and the sine function (sin), i.e., Cot(x) = cos(x)/sin(x).

To find the derivative of the cotangent function, we need to find the derivative of both the numerator (cos(x)) and the denominator (sin(x)) separately using the chain rule and then apply the quotient rule.

The derivative of cos(x) is -sin(x) and the derivative of sin(x) is cos(x).

Now, applying the quotient rule:

(d/dx) [Cot(x)] = ( [-sin(x)] * sin(x) – cos(x) * cos(x) ) / [sin(x)]^2

= -sin^2(x) – cos^2(x) / sin^2(x)

= -[1 / sin^2(x)]

= -csc^2(x)

Therefore, the derivative of the cotangent function (Cot(x)) is -csc^2(x), where csc(x) represents the cosecant function.

##### More Answers:

Understanding the Chain Rule | Derivative of sin(x) with respect to x is cos(x)How to Find the Derivative of cos(x) with Respect to x

Finding the Derivative of the Secant Function | Explained Step-by-Step with Quotient Rule