Derivative of a Quotient of Functions Examples

Find the derivative of the function

We can think of h as the quotient  where

f(x) = x²

and

g(x) = sin x.

Then, using the quotient rule,

Find the derivative of

We'll apply the quotient rule, remembering to take the derivative of the numerator first:

We recommend leaving the answer like this.

What is the derivative of the following function?

Since the denominator is a constant, we can rewrite this function as

To find the derivative we use the multiplication-by-a-constant rule, and the fact that the derivative of a sum is the sum of the derivatives: