$\phi$

${\phi }_x$

${\phi }_{xx}$

MQ: ${\left(r^2+c^2\right)}^{1/2}$

$\pm \frac{r}{{\left(r^2+c^2\right)}^{1/2}}$

$\frac{c^2}{{\left(r^2+c^2\right)}^{1/2}}$

TPS: $r^{2\beta }\ln r$

$\pm \left(2\beta \ln r+1\right)r^{2\beta -1}$

$\pm \left(2\beta \left(2\beta -1\right)\ln r+4\beta -1\right)r^{2\beta -2}$

Cubic: $r^3$

$\pm 3r^2$

6r