How to Find the Derivative of csc(x) Using the Quotient Rule

d/dx csc(x)

To find the derivative of csc(x), we will use the quotient rule

To find the derivative of csc(x), we will use the quotient rule.

The quotient rule states that for a function f(x) = g(x) / h(x), the derivative is given by:

f'(x) = (g'(x) * h(x) – g(x) * h'(x)) / (h(x))^2

In this case, g(x) = 1 and h(x) = sin(x).

Let’s find the derivatives of g(x) and h(x):

g'(x) = 0 (the derivative of a constant is zero)
h'(x) = cos(x) (the derivative of sin(x) is cos(x))

Now substituting these values in the quotient rule formula, we get:

f'(x) = (0 * sin(x) – 1 * cos(x)) / (sin(x))^2
= -cos(x) / sin^2(x)

Therefore, the derivative of csc(x) is -cos(x) / sin^2(x).

More Answers:

Understanding Zero Slope in Mathematics: Definition, Calculation, and Examples
Understanding the Quotient Rule: Finding the Derivative of the Tangent Function
Discover the Derivative of Sec(x) Using the Quotient Rule

Error 403 The request cannot be completed because you have exceeded your quota. : quotaExceeded

Share:

Recent Posts

Mathematics in Cancer Treatment

How Mathematics is Transforming Cancer Treatment Mathematics plays an increasingly vital role in the fight against cancer mesothelioma. From optimizing drug delivery systems to personalizing

Read More »