# Question Video: Finding the First Partial Derivative of a Multivariable Function of Two Variables Mathematics

Find the first partial derivative with respect to π₯ of the function π(π₯, π¦) = π₯ + 2π¦.

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### 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. So here, thatβs π₯ and π¦. Weβre being asked to find the first partial derivative with respect to π₯ of our function. So we denote that as shown using these sort of swirly dβs.

Essentially, when weβre finding the first partial derivative with respect to π₯, weβre interested in saying how the function changes as we let just one of the variables change, as we let π₯ change. So we hold all the other variables constant. So letβs see what that might look like. And weβre going to treat this term by term.

The derivative of π₯ with respect to π₯ is just one. Now, remember, weβre holding π¦ constant. So we differentiate as if π¦ is a constant. And then the derivative of two π¦ with respect to π₯ must be zero. And that means the first partial derivative with respect to π₯ of our function π of π₯, π¦ is one.