Find the Derivative - d/dx csc(2x)

Problem

d(csc(2*x))/d(x)

Solution

1. Identify the outer function as csc(u) and the inner function as u=2*x

2. Apply the chain rule, which states that (d(ƒ)*(g(x)))/d(x)=ƒ′*(g(x))⋅g(x)′

3. Differentiate the outer function csc(u) with respect to u which results in −csc(u)*cot(u)

4. Differentiate the inner function 2*x with respect to x which results in 2

5. Combine the results by multiplying the derivative of the outer function by the derivative of the inner function.

6. Simplify the expression by placing the constant coefficient at the front.

Final Answer

d(csc(2*x))/d(x)=−2*csc(2*x)*cot(2*x)

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