Quotient Rule
The quotient rule is a formula used in calculus to find the derivative of a quotient of functions
The quotient rule is a formula used in calculus to find the derivative of a quotient of functions. It allows us to find the rate at which the value of a function is changing with respect to its independent variable.
Let’s say we have two functions, u(x) and v(x), and we want to find the derivative of their quotient u(x)/v(x).
The quotient rule states that the derivative of u(x)/v(x) is given by:
(u'(x)v(x) – u(x)v'(x)) / [v(x)]^2
Here, u'(x) represents the derivative of u(x) with respect to x, and v'(x) represents the derivative of v(x) with respect to x.
To apply the quotient rule, we follow these steps:
1. Differentiate u(x) with respect to x and denote it as u'(x).
2. Differentiate v(x) with respect to x and denote it as v'(x).
3. Multiply u'(x) by v(x).
4. Multiply u(x) by v'(x).
5. Subtract the results obtained in steps 3 and 4.
6. Divide the result obtained in step 5 by [v(x)]^2.
To summarize, the quotient rule provides us with a way to find the derivative of a quotient by taking the difference of the products of the first function’s derivative with the second function, and the first function with the second function’s derivative, and then dividing it by the square of the second function.
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