(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Evaluate the partial derivatives ∂f/∂x and ∂f/∂y at the origin (0,0), where:

f(x,y) = ((xy)^3/2)/(x^2 + y^2) if (x,y) ≠ (0,0);

and f(0,0) = 0.

2. Relevant equations

∂f/∂x(x0,y0) = lim(h->0) [(f(x0+h, y0) - f(x0, y0)) / h]

∂f/∂y(x0,y0) = lim(h->0) [(f(x0, y0+h) - f(x0, y0)) / h]

3. The attempt at a solution

When I tried to use the definition for ∂f/∂x I got lim(h->0) (0/h^3), and the same result for ∂f/∂y. Is it correct to say therefore the partial derivatives at the origin are zero?

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# Homework Help: Partial Derivatives question

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