Calculus • Step-by-Step

Derivative of cot(x) with Steps

Step-by-step derivative of cot(x). Shows quotient rule derivation on cos(x)/sin(x) proving that d/dx[cot(x)] = -csc²(x) with clear step-by-step math.

Problem Statement

\frac{d}{dx}[\cot(x)]

Final Result

f'(x) = -\frac{\mathrm{sec}\left(x\right)^{2}}{\mathrm{tan}\left(x\right)^{2}}

Formula Required: Cotangent Derivative Rule

Differentiating cos(x)/sin(x) with quotient rule yields -1/sin²(x) = -csc²(x).

\frac{d}{dx}[\cot(x)] = -\csc^2(x)

2 Steps

Set up the differentiation problem with respect to variable $x$.

\frac{d}{dx} \left[ \mathrm{cot}\left(x\right) \right]

Apply the Power Rule to compute the derivative.

\frac{d}{dx} \left[ \mathrm{cot}\left(x\right) \right] = -\frac{\mathrm{sec}\left(x\right)^{2}}{\mathrm{tan}\left(x\right)^{2}}

Interactive Calculator

Enter any equation like 2x + 8 = 20 or x² - 5x + 6 = 0 to get step-by-step solutions.

Writing cot(x) = cos(x)/sin(x) and applying the quotient rule gives (-sin²x - cos²x)/sin²x = -(sin²x + cos²x)/sin²x = -1/sin²x = -csc²(x).