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

Problem

d(csc(h(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=h(x)

2. Apply the chain rule, which states that the derivative of ƒ*(g(x)) is ƒ′*(g(x))⋅g(x)′

3. Differentiate the outer function with respect to its argument. The derivative of csc(u) is −csc(u)*cot(u)

4. Substitute h(x) for u and multiply by the derivative of the inner function, h(x)′

Final Answer

d(csc(h(x)))/d(x)=−csc(h(x))*cot(h(x))*h(x)′

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