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What is the Derivative of xy? - How-To & Steps

What is the Derivative of xy? - How-To & Steps
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  • 0:00 The XY Derivative Steps
  • 2:05 The Solution
  • 2:15 Practical Applications
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Lesson Transcript
Instructor: Yuanxin (Amy) Yang Alcocer

Amy has a master's degree in secondary education and has taught math at a public charter high school.

Read this how-to lesson and you'll see how easy it is to find the derivative of xy. You'll learn the single step that you need to take along with the two rules that are used in this single step.

The XY Derivative Steps

In this lesson, you'll learn how to find the derivative of xy. The derivative in math terms is defined as the rate of change of your function. So, taking the derivative of xy tells you just how fast your function is changing at any point on the graph. The faster the function's curve goes down or up, the higher the value of its derivative at that point will be also.


xy derivative


Thinking of it in this way, your derivative is essentially your slope.

To take the derivative of the function xy, just follow this step. That's right, you only have one step to follow.

Step 1: Use the product rule.

The first step you'll need to take is to use the product rule. This rule tells you what to do when you are trying to take the derivative of the product of two functions. The product rule says that if you have two functions f and g, then the derivative of fg is fg' + f'g.


xy derivative


To use this formula, you'll need to replace the f and g with your respective values. In this case, your f is x and your g is y. So, following this formula, you get the one you're looking at on screen now:


xy derivative


Since y is your function, you have to leave the derivative of y as the derivative of y (y') since you don't know what it is. However, since you are taking the derivative with respect to x, you know what the derivative of x equals (x' = 1). This comes from using the power rule where the derivative equals the exponent multiplied by the variable to the exponent minus 1 (x' = 1x0 = 1).

The Solution

And thus, your answer is xy' + y.


xy derivative


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