To make more sense of what you are doing you need to calculate the volume:

.

This is the calculation of .

So you have, correctly, what I might denote:

and .

These are, respectively, the error in calculation of due to the error in the measurement of , and the error in the calculation of due to the error in the measurement of .

Therefore we further approximate the error in the calculation of the volume, due to the errors in measurement as:

,

and full marks would be given for:

,

in other words:

. Full marks.

In an ideal world you can do things slightly better.

The approximation of the error is rough, however, and it is good practise to round the error to one significant figure:

.

Round to the same precision… it already is… and consider presenting as

.

Then consider:

.

Then consider that maybe might not be the optimal unit. Note that

, so an even better presentation might be:

.

But remember, I will give full marks for

.

Regards,

J.P.

.

, and is the exponential function.

If we are finding , this is differentiating with respect to , while keeping all other variables constant.

So with respect to we see:

So kind of like, say, in one variable calculus:

,

we have

,

as the derivative of is itself.

Regards,

J.P.

I am stuck with this partial differentiation question. Question is

,

and they want .

Can you help me with this?

Thanks ! Regards.