Understanding the Derivative of Cot(x) | Using the Chain Rule and Reciprocal Function Derivatives

(cotx)’

To find the derivative of cotx, we can use the chain rule and the derivative of its reciprocal function

To find the derivative of cotx, we can use the chain rule and the derivative of its reciprocal function.

Recall that cotx is equal to 1/tanx.

Let’s start by finding the derivative of tanx. The derivative of tanx is sec^2(x). This can be derived using the quotient rule or by expressing tanx as sinx/cosx and applying the quotient rule.

Next, let’s find the derivative of the reciprocal function 1/u for u = tanx. Using the chain rule, the derivative is given by d(1/u)/dx = -1/u^2 * du/dx.

Now we can combine the two results to find the derivative of cotx:

(cotx)’ = (1/tanx)’ = (1/(tanx))’ = (1/(u))’ = -1/u^2 * du/dx = -1/(tanx)^2 * (tanx)’ = -1/(tanx)^2 * sec^2(x)

Therefore, the derivative of cotx is -sec^2(x)/tan^2(x).

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