First and Second Derivatives

[mmajames]

Homework Statement

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 don't seem right

Homework Equations

Quotient/Chain/Product Rule

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

 

[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) ​

 

[HallsofIvy]

1. Are these three different functions??

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

 

[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

 

[tiny-tim]

f(x)=X²/(x²-16)
(X²-16)(2X)-(X²)(2X)/(X²-16)²
f'(x)=-32X²/(X-16)²

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