Question

Differentiate.

Answer 1

\[f(x)=x/(x+1/x)\]

Answer 2

\[\frac{x}{x+\frac{1}{x}} = \frac{x}{\frac{x^{2}+1}{x}} = \frac{x^{2}}{x^{2}+1}\]
use quotient rule
\[f'(x) = \frac{2x(x^{2}+1) - 2x(x^{2}+1)}{(x^{2}+1)^{2}} = 0\]

Answer 3

I got 0 and they said it is wrong

Answer 4

oops i messed up
the 2nd part on top should be 2x(x^2) = 2x^3

Answer 5

\[=\frac{2x}{(x^{2}+1)^{2}}\]

Answer 6

Thanks that was right...Do you mind helping me with one more?

Answer 7

sure

Answer 8

\[t^2+5/(t^4-4t^2+4)\]

Answer 9

\[= t^{2} + \frac{5}{(t^{2}-2)^{2}}\]
use power rule and chain rule
\[f'(t) = 2t +(2t)(-2)(\frac{5}{(t^{2}-2)^{3}}) = 2t - \frac{20t}{(t^{2}-2)^{3}}\]

Answer 10

it say its wrong

Answer 11

did i set it up right?

Answer 12

i think so

Answer 13

its correct, i just verified it
are you sure its not (t^2 +5) on numerator

Answer 14

thats wat i put

Answer 15

\[f'(t) = \frac{-2t(t^{2}+12)}{(t^{2}-2)^{3}}\]