Calculating Mean Square Error with Differentials

[Dell]

when calculating the mean square error i have been using the differential,

if a length measured is x=2 and the error m_x=+- 0.005

then x=2+-0.005

if i have x+y where y=3, m_y=+-0.02

m_x+y=$$\sqrt{m_y²+m_x²}$$

m_x*y=$$\sqrt{(y*m_x)²+(x*m_y)²}$$

but if i have x^2 does this work the same

for example if the area of a rectangle is x*2x can i say 2x²

m_2x²=4x*m_x

 

[Mark44]

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when calculating the mean square error i have been using the differential,

if a length measured is x=2 and the error m_x=+- 0.005

then x=2+-0.005

if i have x+y where y=3, m_y=+-0.02

m_x+y=$$\sqrt{m_y^2+m_x^2}$$

m_x*y=$$\sqrt{(y*m_x)^2+(x*m_y)^2}$$

but if i have x^2 does this work the same

for example if the area of a rectangle is x*2x can i say 2x²

m_2x²=4x*m_x

I don't know if this is correct or not. I suggest looking at what your formula for m_x*y, and seeing what you get for m_x*x in the formula above.