Differentiate f(x) = x²y³, f : R² --> R. Am I doing this right

" Differentiate the function f : R² --> R given by the equation: f(x) = x²y³ "

It says from R² --> R, so is that basically the same as saying the equation is f(x,y) = x²y³?

In which case the answer would be:

df/dx = 2xy³
df/dy = 3x²y²

Is this right? Do I just write the answer as the two solutions above or is there a way to combine them?

The "f: R^2 --> R" part says that f maps from R^2 to R; in other words, the function f(x, y) takes any two numbers (in this case, x and y), and assigns them a single number (in this case, f(x, y)). Another example is the map from R^2 to R^2 (g:R^2 --> R^2). Such a map takes two real numbers and makes a two-component vector out of them. An example of such a map is f(x, y) = .

As I mentioned in your other question, the derivative of a multi-variable function is a matrix that consists of its partial derivatives.

I hope this helps!
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Write it as a matrix.

Both ur answers are right...since you arnt told differentiate with respect to what, leave both