How to Use the Product Rule in Calculus

In calculus, the product rule can be used to find the derivatives of products of two or more functions in the same equation. From physics to mathematics, the product rule can apply in the classroom as well as for practical applications. By knowing the basic concept of finding derivatives in calculus, you can use the product rule to simplify your equation or solve for a numerical value.

Things You'll Need

• Calculator

Instructions

1. Write down the equation so that you can visualize the function before applying the product rule. For this example, the equation will be y = (4x^2 + 6x + 1) (3x^4 + 6x^2 + 5).

2. Split the function into F(x) and G(x). For example, in the equation y = (4x^2 + 6x + 1) (3x^4 + 6x^2 + 5), the F(x) could be "4x^2 + 6x + 1" and G(x) could be "3x^4 + 6x^2 + 5."

3. Find the derivative of F(x) and G(x). For example, if F(x) = 4x^2 + 6x + 1, the derivative would be F'(x) = 8x + 6. If G(x) = 3x^4 + 6x^2 + 5, the derivative would be G'(x) = 12x^3 + 12x.

4. Plug the values into the product rule formula:

   FG'(x) = F(x)G'(x) = G(x)F'(x).

   From the values found in Steps 2 and 3, your equation after implementing the product rule can look like this:

   FG'(x) = (4x^2 + 6x + 1)(12x^3 + 12x) + (3x^4 + 6x^2 + 5)(8x + 6)

5. Simplify the equation of "FG'(x)" to obtain your final equation. If you have a value for "x," you can plug the "x" value into the equation to obtain a final numerical answer.

References

• University of Tennessee: Visual Calculus - Product Rule
• UC Davis: Differentiation Using the Product Rule
• Analyze Math: Rules of Differentiation of Functions in Calculus