Sunday

March 29, 2015

March 29, 2015

Posted by **Lisa** on Sunday, March 10, 2013 at 5:37pm.

find f'(x) f ''(x) and a formula for f ^ (n) * x.

I found the first and second derivatives but do not know how to make a general equation for this. I have not learnt the Taylor or Maclaurin Series either. Thank you.

- Calculus Derivative- Taylor Series? -
**Reiny**, Sunday, March 10, 2013 at 5:51pmyour first derivative should have been:

y' = -1(x-1)^-2

then y'' = 2(x-1)^-3

y''' = -6(x-1)^-4 ----> the third derivativ

y'''' = 24(x-1)^-5 ----> the 4th derivative

y''''' = -120(x-1)^-6 ---> the 5th derivative

did you notice that the numbers 1 , 2, 6, 24 , 120 are factorials ?

Did you notice that the alternate ±

did you notice that the exponent is -(n+1) for the nth derivative, e.g. , for the 4th derivative the exponent is -5

how about a general derivative expression from the above?

- Calculus Derivative- Taylor Series? -
**Lisa**, Sunday, March 10, 2013 at 6:06pmYes I did get those as my derivatives. Thank you very much for your help Reiny.

I did not know which patterns to look for.

I think that it would be (-1)^n for the alternating neg. and pos.?

Then n! for the factorial? And lastly x^ -(n+1) for the power of x in the denominator?

I got: f^ (n) (x)= (-1)^n * n! * x^ -(n+1) Is this right?

Thank you very much again. I never knew what patterns to help for. Now I know how to do such problems :)

- Calculus Derivative- Taylor Series? -
**Lisa**, Sunday, March 10, 2013 at 6:06pm*look

- Calculus Derivative- Taylor Series? -
**Reiny**, Sunday, March 10, 2013 at 6:27pmgood job

especially the (-1)^n part, good of you to notice that if n is even , the result has to be positive, and if n is odd we need a negative.

(-1)^n will do that

- Calculus Derivative- Taylor Series? -
**Anonymous**, Sunday, March 10, 2013 at 6:53pmThank you!

**Answer this Question**

**Related Questions**

Calculus - Hi~ Thank you for your help! I was trying to work on a problem about ...

Applied Calculus - Find the first and second derivative of the function: x/(7x+...

Calculus - Please.... I need your help! I posted this question yesterday and no ...

Calculus - Taylor #2 - Find the Taylor series for f(x) centered at the given ...

calculus-- need help desperately! - The Taylor series about x=5 for a certain ...

Calculus - I need to find the second derivative of y=x(x-1)^1/2. I found the ...

Calculus - Find the first and second derivatives of the given functions. y=¡î(x...

Calculus - derivatives - Okay, I want to find the derivative of (x^x)^(x^x)... ...

math - I studied derivatives before, but kind of forgot them all, is there a ...

calculus - Differentiate both sides of the double angle identify sin 2x= 2 sin x...