Imagine you're faced with a function like this:

Up to this point in our studies, we’ve primarily focused on straightforward single-variable derivatives. This function, however, involves both x and y on one side of the equation!

Whenever you're faced with a function with **both x and y **on **one side** of the equation, utilize **implicit differentiation** to take the derivative!

## How to solve with implicit differentiation

A general outline of implicit differentiation problems goes as the following:

- Evaluate the derivative on both sides of the expression
- Find all terms that include the derivative of y (dy/dx)
- Isolate the derivative of y (dy/dx) terms on one side of the equation

Let's go through each of these steps in the problem above to learn how to apply implicit differentiation!

### Evaluate the derivative on both sides of the expression

Let's start with the left-side.

#### Left-side

Lucky for us, the left-side of the equation is just y.

To take the derivative of y, we're going to apply the following truth:

Whenever taking the derivative of **y** in implicit differentiation, treat it as** x**. Then, **multiply** it by the derivative of y, a.k.a. **(dy/dx)**!

Let's start by treating this y as x. Simply put, the derivative of x is 1. Therefore, the derivative of y here will be 1 too...

...but wait! We've then gotta multiply this by (dy/dx), since we're taking the derivative of a y term!

That's it for the left-side! Now, let's take the derivative of the right-side.

#### Right-side

To take the derivative of the right side...

...we're going to apply the sum rule. In essence, this means we'll take the derivative of each term here individually.

I’m a Miami University (OH) 2021 alumni who majored in Information Systems. At Miami, I tutored students in Python, SQL, JavaScript, and HTML for 2+ years. I’m a huge fantasy football fan, Marvel nerd, and love hanging out with my friends here in Chicago where I currently reside.