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Wolfram|Alpha behaves strangely with multiple substitutions into derivative

Posted 11 months ago
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Wolfram|Alpha reacts strangely when I try to substitute multiple variables in a derivation to take the kth derivative of f(x).

I've tested all of the individual components of my input, using sin(x) for f(x), and all of them work on their own:

Multiple substitution:

x*k /. {x->2, k->3}

results in:

Multiple substitution

as expected, returning 2*3.

Substitution for x into the derivative:

D[Sin[x], {x,3}] /. {x->0}

results in:

Substitution for x into the derivative

again, as expected, returning the 3rd derivative of sin(x) at x=0.

Substitution for k into the derivative:

D[Sin[x], {x,k}] /. {k->3}

results in:

Substitution for k into the derivative

once again, as expected, returns the kth derivative of sin(x), where k=3.

But if I combine these and try to substitute both x AND k in the derivative:

D[Sin[x], {x,k}] /. {x->0, k->3}

then Wolfram|Alpha gives up and spits out this:

Substitution for k and x into the derivative

which is a useless regurgitation of its interpretation of the input. What gives? Is there any way I can make this actually work properly?

Posted 11 months ago

If you're evaluating Wolfram Language code, why not do so in Mathematica, the Wolfram Engine, or the Wolfram Cloud (or some other WL environment)?

I always treated Wolfram|Alpha handling any raw WL code as me getting lucky rather than a feature I can expect to work.

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