Question

Please help!!
The area of a rectangle with dimensions x and y is A(xy)=xy. Find the differential of this function.
dA=

If you measure x=6 and y=10, with a measurement error of +/- 0.16, use the differential to estimate the possible error in the caculated area. (Assume that all expressions are in cm. Do not include units in your answer.)
possible error =

Answer 1

I go the first part to equal ydx+xdy but idk what to do for the second part

Answer 2

got*

Answer 3

@jonnymiller can you please help?

Answer 4

is this differential equations?

Answer 5

no its multivariable variables

Answer 6

sorry, I have no idea how to do this

Answer 7

its ok thank you

Answer 8

Think of the differential equation as saying the change in A = y times the change in x + x times the change in y.\[\Delta A = y * \Delta x + x * \Delta y.\] Plug your x and y values into their appropriate x and y variables. The change in x could be as much as + or - .16. So plug .16 in delta y and delta x.
\[\Delta A = 10(\Delta 0.16) + 6(\Delta 0.16)\]

There are questions (on psets/exams) later on in the course that use this concept.

Answer 9

thank you!