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Chain Rule : Finding Where f is Differentiable

Using the chain rule, show that if z = y + f(x^2 - y2), where f is differentiable, then partial derivatives
y(dz/dx) + x(dz/dy) = x

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The chain rule is used to find where a function is differentiable. The solution is detailed and well presented. The response received a rating of "5/5" from the student who originally posted the question.