Question

check my math please
differentiate f(x)=((x)/x^3+1)^6

Answer 1

i got this

Answer 2

Figured it out?

Answer 3

\[6((x)/(x^3+1))^5(-2x^3+1)/(x^3+1)^2\]

Answer 4

i just want u to check my answer please :D

Answer 5

otherwise correct me pls :D

Answer 6

is that the guy from digimon :D?

Answer 7

it looks fabulous but you could also use log differentiation

Answer 8

they havn't teach me that yet :D

Answer 9

finish what you are typing i got another question :)

Answer 10

for sin(x+y)=2x-2y if i differentiate this i would get cos(x+y)+1+y' = 2-2y' right ?

Answer 11

then it says find the equation of the tangent line at the point (pi,pi). and write in slope intercept form

Answer 12

should i substitute cos(pi+pi)+1+y' = 2-2y' and solve for y'?

Answer 13

\[y=(\frac{x}{x^3+1})^6 \\ \ln(y)=6 \ln(\frac{x}{x^3+1}) \\ \ln(y)=6(\ln(x)-\ln(x^3+1)) \\ \ln(y) =6\ln(x)-6\ln(x^3+1) \]
now apply that d/dx ln(u)=u'/u
so we have
\[\frac{y'}{y}=6 \frac{1}{x}-6 \frac{3x^2}{x^3+1} \\ \frac{y'}{y}=\frac{6}{x}-\frac{18x^2}{x^3+1} \\ \]
You could multiply y on both sides and call it quits
or multiply y on both sides then replace y with what you had in the first line
we could also do a little more work like combining fractions first...
\[\frac{y'}{y}=\frac{6(x^3+1)-18x^2(x)}{x(x^3+1)} \\ \frac{y'}{y}=\frac{-12x^3+6}{x(x^3+1)} \\ \text{ multiply y on both sides } y' =y \frac{-12x^3+6}{x(x^3+1)} \\ \text{ recall } y=(\frac{x}{x^3+1})^6 \\ y'=(\frac{x}{x^3+1})^6 \cdot \frac{-12x^3+6}{x(x^3+1)} \\ y'=6 \frac{x^5}{(x^3+1)^6} \frac{-2x^3+1}{x^3+1} \\ y'=6(\frac{x}{x^3+1})^5\frac{-2x^3+1}{(x^3+1)^2}\]
just trying to show you get the exact same thing

Answer 14

now back to your other question

Answer 15

it looks like you tried to use chain rule but ummm...

Answer 16

kinda not entirely but yeah kinda failed just a smidgen

Answer 17

copying and pasting:
"for sin(x+y)=2x-2y if i differentiate this i would get cos(x+y)+1+y' = 2-2y' right ?"
you should put a multiplication operator between cos(x+y) and (1+y')

Answer 18

that is chain rule does derivative of outside +derivative of inside
it says derivative of outside*derivative of inside

Answer 19

that is you should have cos(x+y)*(1+y')=2-2y'

Answer 20

i see

Answer 21

and yes you can replace x with pi and y with pi
and solve for y'

Answer 22

and y' at (pi,pi) will be the slope of your line

Answer 23

cool thanks :D