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$${p} = \frac{4m}{πtd^2}$$

How can I find the error in this formula? I don't know where to begin. I know that I'm looking for the "partial derivative" of density to solve this, but that is a brand new concept for me, which I don't fully understand.

$$p=density$$ $$ m=mass$$ $$t=thickness$$

$$ d=diameter$$

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user106039
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Consider a function $f$ of variables $x_1, x_2, \ldots$. If you assume your input quantities' errors are uncorrelated, then the variance of the output is given by the standard error propagation formula $$ \sigma_f^2 = \left(\frac{\partial f}{\partial x_1}\right)^2 \sigma_{x_1}^2 + \left(\frac{\partial f}{\partial x_2}\right)^2 \sigma_{x_2}^2 + \ldots. $$

I gave a more direct proof of this here, using just basic probability and no linear algebra. You should read through and understand some proof or another -- there is no reason to just take this formula on faith.

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