Derivative of cot(x) with respect to x: Explained with Quotient Rule and Chain Rule

d/dx cot(x)

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

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

The cotangent function can be written as cot(x) = cos(x)/sin(x).

Let’s differentiate the numerator and denominator separately:

Numerator:
d/dx(cos(x)) = -sin(x) (by applying the chain rule)

Denominator:
d/dx(sin(x)) = cos(x) (by applying the chain rule)

Now, applying the quotient rule:

d/dx(cot(x)) = (denominator * numerator’ – numerator * denominator’) / (denominator^2)

= (cos(x) * (-sin(x)) – (-sin(x)) * cos(x)) / sin(x)^2
= (-cos(x)sin(x) + sin(x)cos(x)) / sin(x)^2
= 0 / sin(x)^2
= 0

Therefore, the derivative of cot(x) with respect to x is 0.

More Answers:

Understanding the Quotient Rule: Finding the Derivative of the Tangent Function
Discover the Derivative of Sec(x) Using the Quotient Rule
How to Find the Derivative of csc(x) Using the Quotient Rule

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