Question

x^2+xy-y^2=4 implicit differentiation?

Answer 1

diff wrt to wat?

Answer 2

Find by implicit differentiation

Answer 3

lemme show u something when your nomally have
\[y=f(x)\\
and~ you~ do~ \frac {d}{dx} ~to ~both ~sides\\
\frac {d}{dx}(Y)=\frac {dy}{dx}=\frac {df}{dx}\\
similarily\\
\frac {d}{dx}(f(y))=\frac {df(y)}{dx} * \frac {dy}{dx}, ~ by~the ~chain ~rule\]

Answer 4

follow these rules and differentiate

Answer 5

suppose y=g(x)

Answer 6

rewrite your whole equation like this

Answer 7

x^2xy-y^2=4
x^2x*g(x)-g(x)^2=4
now let side is just some function of x, apply chainrule and other rules you know to differentiate wrt to x

Answer 8

no i had a typo my bad

Answer 9

i was supposed to have a +* in between x^2 and xy

Answer 10

kk just carry on same rules apply

Answer 11

where ever you see a f(y) you have to do f'(y) * y'

Answer 12

and then for the f(x) you are doing the samething as before

Answer 13

and for the right side the any constant differentiated wrt to any variable is just zero

Answer 14

so 2x+xy'-2y*y'=0

Answer 15

product rule for xy

Answer 16

d/dx (xy)=1*y + x*y'

Answer 17

because
d/dx ( x*f(x)) = 1*f(x) + x*f'(x)

Answer 18

so when ever you have ;like lets say 4xy
we use the product rule

Answer 19

yah you think of 4x as a function and y as af unction

Answer 20

d/dx (f(x) G(x)) = f'*(x) *G(x) +f(x) * G'(x)

Answer 21

ok i get it now
i got y'=2x+y/2y-x

Answer 22

ok

Answer 23

Refer to the three statement solution using the Total Derivative with Mathematica 9.

Answer 24

@robtobey
mathematica = wolfram?

Answer 25

Yes. Special pricing for students and I believe faculty.
Current version is Mathematica 10.
http://www.wolfram.com/mathematica/pricing/students.php