Question
Find all points where the first-order partial derivatives of the functions are continuous. Then use Theorems 12.28 and 12.31 to determine the sets in which the functions are differentiable.$$f(x, y)=\frac{x}{y^{2}}$$
Step 1
The partial derivative with respect to $x$ is given by: $$ \frac{\partial f}{\partial x} = \frac{1}{y^{2}} $$ and the partial derivative with respect to $y$ is given by: $$ \frac{\partial f}{\partial y} = -\frac{2x}{y^{3}} $$ Show more…
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Find all points where the first-order partial derivatives of the functions are continuous. Then use Theorems 12.28 and 12.31 to determine the sets in which the functions are differentiable. $$ f(x, y)=x^{2}-y^{2} $$
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