Question

Calculate all four second-order partial derivatives of \(f(x, y) = 13 \sin\left(\frac{x}{y}\right)\) and check that \(f_{xy} = f_{yx}\). Assume the variables are restricted to a domain on which the function is defined. \(f_{xx} = \frac{-13 \sin\left(\frac{x}{y}\right)}{y^2}\) \(f_{xy} = \frac{-13 x \cos\left(\frac{x}{y}\right)}{y^2}\) \(f_{yx} = \frac{-13 x \cos\left(\frac{x}{y}\right)}{y^2}\) \(f_{yy} = \frac{13 x \left(x \sin\left(\frac{x}{y}\right) - 2 y \cos\left(\frac{x}{y}\right)\right)}{y^4}\)

          Calculate all four second-order partial derivatives of
\(f(x, y) = 13 \sin\left(\frac{x}{y}\right)\) and check that \(f_{xy} = f_{yx}\). Assume the variables
are restricted to a domain on which the function is defined.
\(f_{xx} = \frac{-13 \sin\left(\frac{x}{y}\right)}{y^2}\)
\(f_{xy} = \frac{-13 x \cos\left(\frac{x}{y}\right)}{y^2}\)
\(f_{yx} = \frac{-13 x \cos\left(\frac{x}{y}\right)}{y^2}\)
\(f_{yy} = \frac{13 x \left(x \sin\left(\frac{x}{y}\right) - 2 y \cos\left(\frac{x}{y}\right)\right)}{y^4}\)

Calculate all four second-order partial derivatives of
f(x, y) = 13 sin((x)/(y)) and check that fxy = fyx. Assume the variables
are restricted to a domain on which the function is defined.
fxx = (-13 sin((x)/(y)))/(y^2)
fxy = (-13 x cos((x)/(y)))/(y^2)
fyx = (-13 x cos((x)/(y)))/(y^2)
fyy = (13 x (x sin((x)/(y)) - 2 y cos((x)/(y))))/(y^4)

Added by Willie R.

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