Maclaurin sin 2x

Using this general formula, derive the Maclaurin expansion of sin 2x.

The sequence of steps is very similar to the sin x derivation that was shown earlier. Since sin 0 = 0, it is the cosine derivatives, which will yield a result. However, the pattern is very simple as you can see.

This is the first derivative.

This is the second derivative.

This is the third derivative.

This is the fourth derivative.

As you can see, the pattern is a simple one with alternating signs.

We substitute the values into the general formula to find the expansion series of sin 2x.

If you had taken the series expansion of sin x and replaced x by 2x, then the result would have been the same, however I decided to do this the long way so that students can see better.