Derivative of csc(x): Step-by-Step Guide & Explanation

d/dx(cscx)

csc(x)cot(x)

To find the derivative of csc(x) with respect to x, we can use the chain rule. The derivative of csc(x) can be written as:

d/dx(csc(x))

Let’s rewrite csc(x) in terms of sine:

csc(x) = 1/sin(x)

Now, let’s differentiate both sides of the equation using the quotient rule:

d/dx(csc(x)) = d/dx(1/sin(x))

Using the quotient rule, the derivative of 1/sin(x) can be written as:

d/dx(1/sin(x)) = (sin(x)(0) – 1(cos(x)))/(sin(x))^2

Simplifying the expression further:

= -cos(x)/(sin(x))^2

So, the derivative of csc(x) with respect to x is -cos(x)/(sin(x))^2.

This means that at any given value of x, the rate of change of csc(x) with respect to x is equal to -cos(x) divided by the square of sin(x).

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