Question
Evaluate $\bar{f}_{X}$ and $f_{y}$ at the given point.$$f(x, y)=\arctan \frac{y}{x}, \quad(2,-2)$$
Step 1
We treat y as a constant and differentiate with respect to x. Using the chain rule, we get: $$f_{x}(x, y) = \frac{1}{1 + \left(\frac{y}{x}\right)^{2}} \cdot \frac{d}{dx} \left(\frac{y}{x}\right) = \frac{1}{1 + \frac{y^{2}}{x^{2}}} \cdot Show more…
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