# Taylor series to find value of nth derivative

1. Oct 21, 2014

### Panphobia

1. The problem statement, all variables and given/known data
If f(x) = x^5*cos(x^6) find f40(0) and f41(0)

3. The attempt at a solution
So we are supposed to get the Taylor series and use that to get the value of the derivatives I just manipulated the Taylor series for cosx to get the one for this. Would the value be the coefficient?

2. Oct 21, 2014

### RUber

You are evaluating the 40th and 41st derivatives at 0. I am not seeing how this is related to the Taylor series.

3. Oct 21, 2014

### Panphobia

Well this unit is all about Taylor series, and in class he told us to use the Taylor series to get the values of the 40th and 41st derivatives at 0.

4. Oct 21, 2014

### RUber

Once you have. The full Taylor series for f(x), you should be able to tell what 40 derivatives would do. Evaluating at 0 will leave only one term.

5. Oct 22, 2014

### vela

Staff Emeritus
Not quite. What's the general formula for the Taylor series?

6. Oct 22, 2014

### Dick

The value of the derivative f40(0) is the 40th derivative of the x^40 term in the Taylor series. Similar for f41(0). So, no, it's not just the coefficient. Taking the 40 derivatives will give you an extra factorial.

7. Oct 27, 2014

### Panphobia

Yea I figured it out, it is 41!/6!, you have to equate the original taylor series formula to the one for this function, and then solve for the derivative.