Question

i need to find the derivative of f(x)=x^4(1-(2/x+1))

Answer 1

the simplest way is to expand it all out to a sum of terms

Answer 2

f(x)=x^4[1-(2/x+1)]

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

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

[f(x)]' = f'(x)
[x^4]' = 4x^3

[- 2x^4/(x+1)]' = (x+1)[-2x^4]' - (-2x^4)[x+1]'
-------------------------
(x+1)^2

-8x^4 -8x^3 +2x^4
= -------------------
(x+1)^2

Answer 3

-6x^4 -8x^3
f'(x) = 4x^3 + ------------
(x+1)^2

4x^3(x+1)^2 -6x^4 -8x^3
f'(x) = -------------------------
(x+1)^2


4x^3(x^2+2x+1) -6x^4 -8x^3
f'(x) = ---------------------------
(x+1)^2


4x^5 +8x^4 +4x^3 -6x^4 -8x^3
f'(x) = -----------------------------
(x+1)^2


\(4x^5 +2x^4 -4x^3\)
f'(x) = ---------------
\((x+1)^2\)

Answer 4

if I kept track of it that shuld be good

Answer 5

oh my gosh that is awesome help thank you so much!