Question

Find the first partial derivatives of the function. f(r,s) = r ln(r^2+s^2).

Answer 1

Answer:

There are two first partial derivatives of $f(r,s) = r\cdot \ln (r^{2}+s^{2})$: $\frac{\partial{f}}{\partial {r}} = \ln(r^{2}+s^{2}) + \frac{2\cdot r^{2}}{r^{2}+s^{2}}$ and $\frac{\partial {f}}{\partial{s}} = \frac{2\cdot r\cdot s}{r^{2}+s^{2}}$.

Step-by-step explanation:

Let be $f(r,s) = r\cdot \ln (r^{2}+s^{2})$. 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:

$\frac{\partial{f}}{\partial {r}} = \ln(r^{2}+s^{2}) + \frac{2\cdot r^{2}}{r^{2}+s^{2}}$

$\frac{\partial {f}}{\partial{s}} = \frac{2\cdot r\cdot s}{r^{2}+s^{2}}$