How to Find the Derivative of Cot(x): Step-by-Step Guide and Explanation

Dx {cot x}=?

To find the derivative of cot(x), we will use the quotient rule

To find the derivative of cot(x), we will use the quotient rule.

The quotient rule states that if we have a function expressed as f(x) = g(x)/h(x), the derivative of f(x) is given by:

f'(x) = (g'(x)h(x) – g(x)h'(x))/(h(x))^2

Now, let’s apply the quotient rule to find the derivative of cot(x).

We can write cot(x) as a quotient: cot(x) = cos(x)/sin(x).

Let’s assign g(x) = cos(x) and h(x) = sin(x).

Now, let’s calculate the derivatives of g(x) and h(x).

g'(x) = -sin(x) (derivative of cos(x) is -sin(x))

h'(x) = cos(x) (derivative of sin(x) is cos(x))

Now, we substitute the derivatives into the quotient rule:

cot'(x) = (g'(x)h(x) – g(x)h'(x))/(h(x))^2

= (-sin(x)*sin(x) – cos(x)*cos(x))/(sin(x))^2

= -(sin^2(x) + cos^2(x))/(sin^2(x))

= -1

Therefore, the derivative of cot(x) is -1.

More Answers: