### Video Transcript

Find the first partial derivative with respect to π¦ of the function π of π₯, π¦ equals π₯ plus two π¦.

This is a multivariable function, a function in terms of more than one variable. Here, thatβs π₯ and π¦. Weβre looking to find the first partial derivative with respect to π¦ of our function. And we denote that as shown. Now, the reason we use this curly β is because weβre looking to see how our function changes as we let just one of the variables change. In this case, thatβs π¦. And we hold all the others constant. So we change the variable π¦ and we treat π₯ as a constant here.

So letβs go term by term. The first term in our function is π₯. Remember, weβre finding the first partial derivative with respect to π¦. So we treat π₯ as a constant. And we know when we differentiate a constant with respect to π¦, we get zero. Then, the second term is two π¦. We know that when we differentiate two π¦ with respect to π¦, we get two. And zero plus two is two.

The first partial derivative with respect to π¦ of the function π of π₯, π¦ equals π₯ plus two π¦ is two.