\(f(x, y) = 5x - 17y\)
\(f_x = 5\)
\(f_y = -17\)
\(f_xx = 0\)
\(f_yy = 0\)
\(f_xy = 0\)
\(f_yx = 0\)
\(f(x, y) = 3x^2 + 1\)
\(f_x = 6x\)
\(f_y = 0\)
\(f_xx = 6\)
\(f_yy = 0\)
\(f_xy = 0\)
\(f_yx = 0\)
\(f(x, y) = ln(x^2 + y)\)
\(f_x = \frac{2x}{x^2 + y}\)
\(f_y = \frac{1}{x^2 + y}\)
\(f_{xx} = \frac{-2x^2 + 2y}{(x^2 + y)^2}\)
\(f_{yy} = - \frac{1}{(x^2 + y)^2}\)
\(f_{xy} = - \frac{2x}{(x^2 + y)^2}\)
\(f_{yx} = - \frac{2x}{(x^2 + y)^2}\)
I found questions 22 and 23 were very simple cases. I hope I did not miss anything in these two questions. In question 24, the derivatives were challenging. I am unsure if \(f_{xy}\) and \(f_{yx}\) should be equal like I found. If you find an issue with my solutions, please let me know. Thank you!
I learned how to use latex in R. This will be useful in the future when I need to show equations in future projects or when presenting information in a job.
I learned calculus to much greater detail than I have used it before.
The course provided me with many new resources to continue using throughout my degree and career.