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I have a function: $$L_R=4*\pi*5*R^2*J$$ I have error values for this R and J. So I want to find the error of $$L_R$$

Should I go for:$$L_R=f$$ $$df=L_{R_{error}}=\frac{\partial{f}}{\partial{x}}dx+\frac{\partial{f}}{\partial{y}}dy$$ where $$x=R$$$$y=J$$$$dx=J_{error}$$$$dy=R_{error}$$

However, i have no idea what their coefficients would be or how to calculate the error of $$L_R$$

Ege Tunç
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  • Please clarify your specific problem or provide additional details to highlight exactly what you need. As it's currently written, it's hard to tell exactly what you're asking. – Community Aug 08 '23 at 13:32
  • "I have error values for this R and F" - did you mean "R and J"? Might the errors be correlated? This issue is known as propagation of uncertainty or propagation of error – Henry Aug 08 '23 at 13:44
  • @Henry yes J is F. Sorry my bad. For instance my J is 5 and R is 8. J_error is 0.2 and R_error is 0.5. – Ege Tunç Aug 08 '23 at 14:12
  • Or is it just: ΔL = 2 * (ΔR/R) + (ΔJ/J) * L. Where ΔR and ΔJ are errors of R and J, respectively. – Ege Tunç Aug 08 '23 at 14:14

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