# A complicated taylor polynomial

1. Oct 11, 2007

### IMDerek

Is there any nice trick for finding the Taylor polynomial of a composition of 2 functions, both of which can be expressed as taylor polynomials themselves? For example, finding the taylor polynomial for $$e^{\cos x}$$. Thanks.

2. Oct 12, 2007

### AiRAVATA

Well, for example, near [itex]\pi/2[/tex]

$$e^{\cos x}=1+\cos x+ \frac{cos^2 x}{2!}+\frac{\cos^3 x}{3!}+...$$

and

$$\cos x=-\frac{(x-\pi/2)^2}{2!}+\frac{(x-\pi/2)^4}{4!}-...$$

now, the hard part is to compose it, so maybe it's easier to just calculate the derivative and evaluate, depends on what are you looking for.

Last edited: Oct 12, 2007
3. Oct 13, 2007