Thread: a quick question about partial derivatives

When you take the partial derivative of

z=x^2y + xy^2 , x=2+t^4 , y= 1-t^3

you get 4(2xy+y^2)t^3 - 3(x^2+2xy)t^2

do you have to plug "2+t^4" in for each x and "1-t^3" in for each y?

Why or why not?

I was under the assumption that you needed to leave the answer in the same variable, in this case "t".

In our case, we are calculating not a partial derivative of but the ordinary derivative of with respect to . To answer your question, we don't have to replace and with expressions for if we regard them as functions of , as long as we remember that



is a function of one variable, .