csc(x)’ =
The derivative of csc(x) can be found using the quotient rule
The derivative of csc(x) can be found using the quotient rule.
First, let’s express csc(x) as 1/sin(x), where sin(x) is the function in the denominator.
Using the quotient rule, the derivative of 1/sin(x) is:
[ (sin(x))’ * 1 – (1)’ * sin(x) ] / (sin(x))^2
The derivative of sin(x) is cos(x), and the derivative of a constant 1 is 0.
So, applying these values to the equation, we get:
[ cos(x) * 1 – 0 * sin(x) ] / (sin(x))^2
Simplifying further, we have:
cos(x) / (sin(x))^2
Finally, we can rewrite this in terms of csc(x):
csc(x) * cot(x)
Therefore, the derivative of csc(x) is csc(x) * cot(x).
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