Question

Determine fxy when f(x, y) = x tan⁻¹ (x/y)

Answer 1

To determine fxy of f(x, y), differentiate f(x, y) with respect to x, then differentiate the result with respect to y, considering y as a constant. The value of fxy is -1/x.

Step-by-step explanation:

To determine the partial derivative fxy, we need to differentiate f(x, y) with respect to y after differentiating with respect to x. Here's the step-by-step process:

1. Take the derivative of f(x, y) with respect to x: f'(x) = tan⁻¹(x/y) + x(-y/x²)
2. Take the derivative of f'(x) with respect to y, considering y as a constant: fxy = (d/dy)(f'(x)) = x(-1/x²) = -1/x

Therefore, the value of fxy is -1/x.