The Quotient Rule: Finding the Derivative of csc(x)

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).

More Answers:

Proving the Derivative of sin(x) is cos(x) using the Limit Definition of Derivative
Understanding the Chain Rule: Finding the Derivative of cosine(x)
Mastering the Quotient Rule: Deriving the Secant Squared of Tan(x)

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