How to Differentiate Functions Using the Quotient Rule
The quotient rule is the rule that tells you how to take the derivative of a function that is a ratio of two differentiable functions.
where u = u(x) and v = v(x)
Note! Sometimes you get lucky, and it’s possible to simplify the answer. Most of the time that’s not possible though, and you can just leave the fraction as it is.
Differentiate the expression 2x + 1 ex
Here, u = 2x + 1 and v = ex. You get u′ = 2 and v′ = ex, which gives you
Differentiate the expression 3x3 − 2x2 + 7 x − 1
Here, you have u = 3x3 − 2x2 + 7 and v = x − 1. That means u′ = 9x2 − 2 and v′ = 1, and the derivative is