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First-Order Derivatives of the Second-Kind Kelvin Function (Graph)

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Calculates a table and plots the first derivatives of the Kelvin functions of the second kind, ker'v(x) and kei'v(x).
Order v
Real numbers
[ Initial values for x
]
\(\normalsize Derivative\ Kelvin\ functions\\ \hspace{60px} of\ the\ 2nd\ kind\ ker_\nu'(x),\ kei_\nu'(x)\\ (1)\ x^2y''+xy'-(ix^2+\nu^2)y=0\\ \hspace{25px} y=c_1{ker_\nu(x)}+ic_2{kei_\nu(x)}\\ (2)\ ker_\nu'(x)={\large\frac{ker_{\nu\tiny +1}(x)+kei_{\nu\tiny +1}(x)}{\sqrt{2}}} +{\large\frac{\nu}{x}}ker_\nu(x)\\ \hspace{25px} kei_\nu'(x)={\large\frac{kei_{\nu\tiny +1}(x)-ker_{\nu\tiny +1}(x)}{\sqrt{2}}} +{\large\frac{\nu}{x}}kei_\nu(x)\\\)

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