Partial Derivatives (Example 1)

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Partial Derivatives (Example 1)

In multivariable calculus you may be asked to find the partial derivatives.

When deriving with respect to a variable, just treat all other variables as a constant.

Example question: Find all first partial derivatives of \(f(x,y) = {y^5} – 3xy\).

Let’s start with the partial derivative with respect to x.

See how there’s only an x term in -3xy? Treat y as a constant.

\[\frac{{\partial f}}{{\partial x}} = – 3y\]

And now let’s find the derivative with respect to y, so now treat x as a constant.

\[\frac{{\partial f}}{{\partial y}} = 5{y^4} – 3x\]

And you’re done. Don’t worry, it’ll get hard soon enough!

Click here to move to the next example and try a harder multi-variable partial derivative next!

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