How to Find the Derivative of csc(x) using the Quotient Rule in Math

d/dx cscx

To find the derivative of the function y = csc(x), we can use the quotient rule

To find the derivative of the function y = csc(x), we can use the quotient rule.

The quotient rule states that if we have a function in the form y = f(x)/g(x), then its derivative is given by:

dy/dx = (f'(x) * g(x) – f(x) * g'(x)) / (g(x))^2.

Here, f(x) = 1 and g(x) = sin(x), since csc(x) is equal to 1/sin(x). Taking the derivatives of the numerator and denominator, we get:

f'(x) = 0 (since the derivative of a constant is zero)

g'(x) = cos(x) (the derivative of sin(x) is cos(x))

Now, we can substitute these values into the quotient rule formula:

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

Simplifying further, we have:

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

We can also rewrite this as:

dy/dx = -cot(x) / sin(x)

Therefore, the derivative of y = csc(x) is -cot(x) / sin(x).

More Answers: