Find the derivative of the function.y = 7 cot n𝜃

To find the derivative of the function y = 7 cot(nθ), we first need to know the derivative of cot(x), which is -csc²(x).

Step 1: Identify the function to differentiate y = 7 cot(nθ)

Step 2: Apply the chain rule The chain rule states that the derivative of a composite function is the derivative of the outer function times the derivative of the inner function.

In this case, our outer function is cot(x) and our inner function is nθ.

Step 3: Differentiate the outer function The derivative of cot(x) is -csc²(x).

Step 4: Differentiate the inner function The derivative of nθ with respect to θ is n.

Step 5: Apply the chain rule So, the derivative of y = 7 cot(nθ) is dy/dθ = -7n csc²(nθ).