Derivatives of functions having different independent variables..?

Question

i need to find d/dt of (x^2+y^2).Should i have to consider X and Y as constants just like partial differentiation is done?

Answer 1

I'm assuming you mean the equation is x^2 + y^2 = 0, but it shouldn't make much of a difference.

First, take the derivative of everything with respect to x to get: 2x + 2y * y' = 0.

Next, bring everything with a y' in it to the left side and everything else to the right. Now you have 2y * y' = 2x.

Now factor out the y' and solve. You get y' = 2x/2y. Just so you know, this is known as implicit differentiation.

Answer 2

you should see x as function of t and y as function of x

( that is convention ! ) it is very well possible that x and y are indeed constants not depending on t

so dy/dt = dy/dx * dx/dt

Answer 3

d/dt (f(u) = d/du f(u) * du/dt

If u = x, then d/dt f(x) = d/dx f(x) * dx/dt

If f(x) = x^2, d/dt f(x) = 2x * dx/dt

Take the derivative w.r.t. t of all terms in your expression using the above formulas.