How do I evaluate this: $$ \frac{d}{dx}\left(\frac{dx}{dt}\right) $$ given that $x$ is function of $t$
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1What are your thoughts, and what have you tried? Is there a specific function $x(t)$ that you're interested in? That will make this easier. – The Count Feb 05 '17 at 16:19
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HINT: Apply the chain rule. – Mark Viola Feb 05 '17 at 16:39
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Do you know how what it means for a function between (possibly infinite dimensional) topological vector spaces to be differentiable? Here I would view $x\mapsto \frac{dx}{dt}$ as a map from $C^\infty(\Bbb R)\to C^\infty(\Bbb R)$, or as a map from $C^1_0(\Bbb R)\to C_0(\Bbb R)$. Is this the kind of context you are expecting? – s.harp Feb 05 '17 at 17:01
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Possible duplicate of Derivative of a function with respect to another function. – Simply Beautiful Art Feb 06 '17 at 00:55
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You will need to use the Chain Rule to express the $d/dx$ with respect to $t$.
$$ \frac{d}{dx}\left(\frac{dx}{dt}\right)=\frac{\frac{d}{dt}\left(\frac{dx}{dt}\right)}{\frac{dx}{dt}} $$
Tim Thayer
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