Problem: Differentiate
\[ e^{\frac {2 r}{\sqrt {a}}} + 3 \left ( \frac {r}{\sqrt {a}} \right )+ \left ( \frac {r}{\sqrt {a}} \right )^2 \]
w.r.t \(\frac {r}{\sqrt {a}}\) to produce \[ 2 e^{\frac {2 r}{\sqrt {a}}} + 3 + 2 \frac {r}{\sqrt {a}} \]
In other words, we want to treat \(\frac {r}{\sqrt {a}}\) as \(x\) in the expression
\[ e^{2 x} + 3 x+ x^2 \]
| Mathematica Clear[p, x, r, a] p[x_] := Exp[2 x] + x^2 + 3*x; v = r/Sqrt[a]; With[{v = x}, Inactive[D][p[v], v]]; Activate[%]; % /. x -> v
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\(\frac {2 r}{\sqrt {a}}+2 e^{\frac {2 r}{\sqrt {a}}}+3\) |
| Maple Credit for the Maple answer goes to an internet post by Carl Love restart; D(x->exp(2*x)+3*x+x^2) (r/sqrt(a));
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\(2\,{{\rm e}^{2\,{\frac {r}{\sqrt {a}}}}}+3+2\,{\frac {r}{\sqrt {a}}}\) |