# First and Second Derivatives

1. Mar 8, 2012

### mmajames

1. The problem statement, all variables and given/known data
f(x)=X^2/(x^2-16)

f(x)=1+x/1-X

f(x)=X^3(X-2)^2

Ive done the first and second derivatives but they just dont seem right

2. Relevant equations
Quotient/Chain/Product Rule

3. The attempt at a solution
f(x)=X^2/(x^2-16)
(X^2-16)(2X)-(X^2)(2X)/(X^2-16)^2
f'(x)=-32X^2/(X^2-16)^2
(X^4-32X^2+256)(-64X)-(-32X^2)(4X^3-64X)/(X^4-32X^2+256)^2
-64x^5+2048X^3-16384X+128X^5-2048X^3
f''(x)=64X^5-16384X/(X^4-32X^2+256)^2

f(x)=1+x/1-X
(1-X)(1)-(1+X)(-1)/(1-X)^2
f'(x)=2-2X/(1-X)^2
(X^2-2X+1)(-2)-(2X-2)(2-2X)/(X^2-2X+1)^2
f''(x)=2X^2+4X+2/(X^2-2X+1)^2

f(x)=X^3(X-2)^2
(X^3)(2X-4)+(3X^2)(X-2)^2
2X^4-4X^3+3X^4-12X^3+12X^2
f'(x)=5X^4-16X^3+12X^2
5X^4-16^3+12X^2
f''(x)=20X^3-48X^2+24X

2. Mar 9, 2012

### tiny-tim

hi mmajames!

eugh! :yuck: this is impossible to read!

try using the X2 button just above the Reply box (and a few more spaces)

3. Mar 9, 2012

### HallsofIvy

Staff Emeritus
1. Are these three different functions??

2. Please use parentheses 1+ x/x+ 3 is not the same as (1+ x)/(x+ 3).

4. Mar 9, 2012

### mmajames

f(x)=X2/(x2-16)
(X2-16)(2X)-(X2)(2X)/(X2-16)2
f'(x)=-32X2/(X-16)2
(X4-32X4+256)(-64X)-(-32X2)(4X3-64X)/(X4-32X2+256)2
-64x^5+2048X^3-16384X+128X5-2048X3
f''(x)=64X5-16384X/(X4-32X^2+256)2

f(x)=(1+x)/(1-X)
(1-X)(1)-(1+X)(-1)/(1-X)2
f'(x)=2-2X/(1-X)2
(-2X+1)(-2)-(2X-2)(2-2X)/(X2-2X+1)2
f''(x)=2X2+4X+2/(X2-2X+1)22

f(x)=X3(X-2)2
(X3)(2X-4)+(3X2)(X-2)2
2X4-4X3+3X4-12X3+12X2
f'(x)=5X4-16X3+12X2
5X^4-163+12X2
f''(x)=20X3-48X2+24X

And yes Three different functions

5. Mar 10, 2012

### tiny-tim

hmm … i can see two mistakes already

sorry, but i'm not checking the rest until you've gone over them again, to find any other mistakes

also, (as HallsofIvy says) please use more brackets