Find the Derivative - d/dx csc(3x)

Problem

d(csc(3*x))/d(x)

Solution

1. Identify the outer function and the inner function to apply the Chain Rule. The outer function is csc(u) and the inner function is u=3*x

2. Apply the derivative formula for the cosecant function, which states d(csc(u))/d(u)=−csc(u)*cot(u)

3. Differentiate the inner function 3*x with respect to x which results in 3

4. Multiply the derivative of the outer function by the derivative of the inner function according to the Chain Rule.

5. Simplify the expression by rearranging the constant factor to the front.

Final Answer

d(csc(3*x))/d(x)=−3*csc(3*x)*cot(3*x)

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