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Wolfram|Alpha behaves strangely with multiple substitutions into derivative

Posted 1 year 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?

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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