\[|J_{\nu}'\left(\nu x\right)|\leq\frac{(1+x^{2})^{\frac{1}{4}}}{x(2\pi\nu)^{%
\frac{1}{2}}}\frac{x^{\nu}\exp\left(\nu(1-x^{2})^{\frac{1}{2}}\right)}{\left(1%
+(1-x^{2})^{\frac{1}{2}}\right)^{\nu}},\]