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I have a function that I want to differentiate, but it has a bunch of constant variables in it, like an unknown radius and velocity with the x in the function as well. For example, $\frac{\pi r + 2x}{v}$, where r is the radius of a circle and v is an unknown velocity. Is there any way to take this derivative, like treating them as constants and doing it normally, such as: $\frac{d}{dx}(\frac{\pi r + 2x}{v}) = \frac{2}{v}?$

Curulian
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  • If they're constants, then they're constants and you do it "normally." If they're variables, you need to consider any dependencies on $x$. – A. Thomas Yerger Jan 13 '22 at 04:24
  • Are you comfortable with the derivative of $\pi$ is $0$ and the derivative of $\pi x$ is $\pi$ and similar? These other constants $r$ and $v$ behave the same. – ndhanson3 Jan 13 '22 at 04:38

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If the value of r and v are fixed (not changing with x), but you do not know what the values are, you should treat them as a constant. In this case, the word "constant variables" is wrong. You can say unknown constants.

However, if they change with the change of x, then you should consider the derivative of v and r with respect to x, which gives u the answer: $\frac{(\pi r^\prime +2)v-(\pi r +2x)v^\prime}{v^2}$

khashayar
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