Exploring the Derivative of csc(x) with Respect to x | Quotient Rule and Chain Rule Methods

(d/dx) cscx

To find the derivative of csc(x) with respect to x, we can use the quotient rule and the chain rule

To find the derivative of csc(x) with respect to x, we can use the quotient rule and the chain rule.

csc(x), which is the reciprocal of sin(x), can also be written as 1/sin(x).

Using the quotient rule, we have:

d/dx (csc(x)) = [(d/dx)(1)](sin(x)) – (1/(sin(x))^2)(d/dx)(sin(x))

The derivative of 1 with respect to x is 0, so the first term becomes 0.

The derivative of sin(x) with respect to x is cos(x).

Now, we substitute these values back into our equation:

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

Simplifying further, we get:

d/dx (csc(x)) = -cos(x) / (sin(x))^2

So, the derivative of csc(x) with respect to x is -cos(x) divided by the square of sin(x).

More Answers: