Answer:
There are two first partial derivatives of [tex]f(r,s) = r\cdot \ln (r^{2}+s^{2})[/tex]: [tex]\frac{\partial{f}}{\partial {r}} = \ln(r^{2}+s^{2}) + \frac{2\cdot r^{2}}{r^{2}+s^{2}}[/tex] and [tex]\frac{\partial {f}}{\partial{s}} = \frac{2\cdot r\cdot s}{r^{2}+s^{2}}[/tex].
Step-by-step explanation:
Let be [tex]f(r,s) = r\cdot \ln (r^{2}+s^{2})[/tex]. The quantity of first partial derivatives of a multivariate function is equal to the number of variables. For this function, there are two first partial derivatives:
[tex]\frac{\partial{f}}{\partial {r}} = \ln(r^{2}+s^{2}) + \frac{2\cdot r^{2}}{r^{2}+s^{2}}[/tex]
[tex]\frac{\partial {f}}{\partial{s}} = \frac{2\cdot r\cdot s}{r^{2}+s^{2}}[/tex]
