Find \(f_x, f_y,f_{xx},f_{yy},f_{xy},f_{yx}\):
\[ f(x,y) = \frac{ln(x)}{4y} \\ f_x = \frac{1}{4xy} \\ f_y = \frac{-ln(x)}{4y^2} \\ f_{xy} = \frac{df_x}{dy} =\frac{d}{dy} \frac{1}{4xy} = \frac{-1}{4xy^2} \\ f_{yx} = \frac{df_y}{dx} =\frac{d}{dx} \frac{-ln(x)}{4y^2} = \frac{-1}{4xy^2} \\ f_{xx} = \frac{df_x}{dx} =\frac{d}{dx} \frac{1}{4xy} = \frac{-1}{4x^2y} \\ f_{yy} = \frac{df_y}{dy} =\frac{d}{dy} \frac{-ln(x)}{4y^2} = \frac{ln(x)}{2y^3} \]
My valuable element was seeing math applied to different fields. There were only a couple of items I had never seen before, but on the other hand, everything I had seen was very focused on Physics. Seeing these mathematics applied elsewhere was very helpful.