# Derivative of infinite series

1. Apr 28, 2012

### cj5892

1. The problem statement, all variables and given/known data
Consider the infinite series s(x)=1-tan^2(x)+tan^4(x)-tan^6(x)+... , where 0<x<pi/4
s'(x)=
A.sin2x
B.cos2x
C.-tan2x
D.-sin2x
E.-cos2x

3. The attempt at a solution

Attempting to derive the series, i get 1-2tanxsec^2x+4tan^3(x)sec^2(x)-6tan^5(x)sec^2(x)+...

am i missing something obvious here? i don't see any trig identities in that that would give any of the answers

2. Apr 28, 2012

### LCKurtz

Hint: Sum that geometric series for s(x) first.

Last edited: Apr 28, 2012
3. Apr 28, 2012

### cj5892

i still can't get it :(

4. Apr 28, 2012

### Dick

What's the series expansion of 1/(1+r)?

5. Apr 28, 2012

### LCKurtz

Or what is the sum of a geometric series with first term a and ratio r?