If you're just starting calculus, perhaps you're asking about using the definition of the derivative to differentiate .
We have
Expand the numerator using the binomial theorem, then simplify and compute the limit.
In general, the derivative of a power function is
. (This is the aptly-named "power rule" for differentiation.)
Answer:
Maximum error for viscosity is 17.14%
Step-by-step explanation:
We know that everything is changing with respect to the time, "r" is changing with respect to the time, and also "p" just "v" will not change with the time according to the information given, so we can find the implicit derivative with respect to the time, and since
The implicit derivative with respect to the time would be
If we multiply everything by dt we get
Remember that the error is given by therefore doing some algebra we get that
Since, r = 0.006 , dr = 0.00025 , p = 4*105 , dp = 2000 we get that
Which means that the maximum error for viscosity is 17.14%.