Calculus Basics | Derivative of cot^(-1)(u) with respect to x using the Chain Rule

d/dx cot^-1 (u)

To find the derivative of the function cot^(-1)(u) with respect to x, we can use the chain rule

To find the derivative of the function cot^(-1)(u) with respect to x, we can use the chain rule. Let’s break down the steps:

Step 1: Identify the composite function
The composite function is cot^(-1)(u).

Step 2: Determine the derivative of the outer function
The derivative of cot^(-1)(u) with respect to u can be computed using the formula:
d/dx (cot^(-1)(u)) = -1 / (1 + u^2).

Step 3: Calculate the derivative of the inner function
To find the derivative of u with respect to x, we use the chain rule and multiply it by du/dx. So, we need to compute du/dx.

Step 4: Combine the derivative of the outer function with the derivative of the inner function
Using the chain rule, we multiply the derivative of the outer function by the derivative of the inner function:
d/dx (cot^(-1)(u)) = -1 / (1 + u^2) * du/dx.

Putting it all together, the derivative of cot^(-1)(u) with respect to x is:
d/dx (cot^(-1)(u)) = -du/dx / (1 + u^2).

Remember to substitute du/dx with its appropriate value depending on the context of the problem.

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