U/V Derivative Rule For Differentiation, When To Use The Quotient Rule For Differentiation

Introduction to the Quotient Rule

The quotient rule is the last of the main rules for calculating derivatives, and it primarily deals with what happens if you have a function divided by another function and you want to take the derivative of that. So let”s start with f(x) = x / x^2. What is the derivative of f(x)? Is it just the top? Is it the bottom? Is it the derivative of the top times the derivative of the bottom? What is it? Well you could simplify this into 1 / x, and then f`(x) would then be -1 / x^2, because 1 / x is the same as x^-1. Then we just use our power rule. But is there a way to find that without simplifying? You won”t be able to simplify in every case. Think about sin(x) / x, or (x^2 + ln(x)) / cos(x). What about those cases? You need to know the quotient rule.


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