Finding the Derivative of csc(x) – How to Use the Chain Rule for Optimization

Derivative of csc(x)

To find the derivative of csc(x), we can use the chain rule

To find the derivative of csc(x), we can use the chain rule.

Recall that the derivative of a function f(g(x)) with respect to x is given by f'(g(x)) multiplied by g'(x).

In this case, our function is csc(x), which can also be written as 1/sin(x).

So, let’s rewrite csc(x) as 1/sin(x).

Using the quotient rule, the derivative of 1/sin(x) is:

[ (sin(x)*0) – (1*cos(x)) ] / (sin(x))^2

Since the derivative of sin(x) is cos(x), and the derivative of 1 (a constant) is 0.

Simplifying the derivative, we get:

– cos(x) / (sin(x))^2

Which can also be written as:

– cot(x) * csc(x).

So, the derivative of csc(x) is -cot(x) * csc(x).

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