How to Do Physics Derivations
When learning a derivation, first write out (in a sentence) each step. It will help you follow the logic and it will help you to develop a style and framework for relations that you will later derive on your own.
Here is an example for the derivation of Euler's relation, 
:
1. Write out the general form of the Maclaurin series.
2. Use
the Maclaurin series to expand: 
.
3. Use
the Maclaurin series to expand 
4.
Rearrange the terms in the expansion of 
grouping the
real terms together and the imaginary terms together.
5.
Compare the expression of 
with the
expansions of 
and 
and rewrite 
as a function
of 
and 
.
The derivation will look like this:
Show that 
.
The general form of the Maclaurin series is:
(1)
Using (1) to
expand 
gives
(2)
(3)
Using (1) to
expand 
to an imaginary
power, where 
gives
(4)
Rearranging (4) we have:
Comparing this with (2) and (3) gives:
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Here is another example:
Show that 
1. Write down the equation showing the relationship of wavelength, frequency and the speed of light.
2. Take the magnitude of the derivative with respect to n .
3.
Separate 
and move one of
the 
of 
over to the
other side.
4.
Substitute the relationship of 
for the 
on the 
side of the
equation.
The actual derivation will look like this:
Show that 
.
For light waves, 
. (1)
Then the magnitude of the
derivative is 
and rearranging gives
. (2)
Using (1) in (2) gives
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