The derivative of the product of two terms is equal to the sum of the product of the first term with the derivative of the second term and the product of the second term with the derivative of the first term, or vice verse.

For example,

The product rule does not apply on

Product Rule of Derivatives |

D ((2x + 1)(x - 1)) = (2x + 1) * D(x - 1) + (x - 1) * D(2x + 1)

- D (x - 1) is equal to D x - D 1 = 1 - 0 = 1
- D (2x + 1) is equal to D 2x + D 1 = 2 + 0 = 2

D ((2x + 1)(x - 1)) = (2x + 1) * 1 + (x - 1) * 2 = 2x + 1 + x - 2 = 3x - 1So the derivative of (2x + 1)(x - 1) is 3x - 1. Note that the above derivative could also be simply done by first multiplying (2x + 1)(x - 1) by FOIL (or simple, just multiplying the two binomials) to get 2x^2 - x - 1, and then applying sum rule of derivatives to get its derivative. This is just to illustrate the product rule.

The product rule does not apply on

- A product of and variables, for example, 2x, 10y,
*e*x, π x - A product of constants, such as 10 * 11

- A product of variables, such as xy, ab, cd
- A product of expressions, such as (x + 1)(x - 1), or (x^2 + 2x + 3)(4x + 1)(1 - x)
- A product of functions, such as f(x) * g(x)
- A product of trigonometric expressions, such as sin(x)cos(x) or (sin x + 1)(cos x - 1)
- A product of logarithmic expressions, such as log(a) * log(b)
- A product of the combination of any of the above mathematical expressions in any order
- A product of more than two terms, in which case you can apply the product rule to two terms each time