Question

find the equation of the tangent line to (e^xy)+(x^2)-(y^2)=5 through the point (2,0)

Answer 1

Looks like an implicit differentiation problem to me, I will first have to give it a try myself though.

Answer 2

\(\large (e^xy)+(x^2)-(y^2)=5 \) OR \(\large (e^{xy})+(x^2)-(y^2)=5 \)
and i agree... implicit diffn....

Answer 3

\[y=\frac{dy}{dx}(x-2)\]

Answer 4

dpalnc it is the second equation you wrote

Answer 5

for the derivative i got: (-2x+(e^xy)y)/(e^xy)x-2y

Answer 6

did anyone get that

Answer 7

If I use implicit differentiation for the 2nd equation that @dpalnc posted I get

\[ \Large e^{xy}\left(y+x\frac{dy}{dx}\right) +2x -2y \frac{dy}{dx}=0\]

Answer 8

Will have to rearrange that a bit @mariaad

Answer 9

i got that too but i thought i had to simplify it

Answer 10

You have to solve for \(\Large \frac{dy}{dx} \)

Answer 11

to find the slope i would have to plug in 2 to that? because it is the derivative?

Answer 12

well first solve for dy/dx, then you can do that. because dy/dx=f'(x) and that is the slope at any given point.

Answer 13

\[ \Large \frac{dy}{dx}=\frac{-2x-ye^{xy}}{xe^{xy}-2y} \] That is what I get after solving for dy/dx, I recommend you to double check though.

Answer 14

yeahh cus i basically got the same thing except on the nominator i got -2x+ye^xy instead of minus

Answer 15

http://www.wolframalpha.com/input/?i=%28e%5Exy%29%2B%28x2%29%E2%88%92%28y2%29%3D5

Answer 16

so now i plug in 2 to that? but i get (-4+e

Answer 17

i got -2..is that what you got?

Answer 18

?

Answer 19

well yes seems correct to me.

Answer 20

okk thank you then for the equation i got y=-2x+4

Answer 21

best thing you could do is feed wolframalpha now with your equations and see if it's correct, if you want to make sure that there is no mistake.

Answer 22

okk thanks again

Answer 23

welcome

Answer 24

just a note:
\[\Large e^{xy}\left(y+x\frac{dy}{dx}\right) +2x -2y \frac{dy}{dx}=0\] you will still need to rearrange to find dy/dx; but at this stage you can input the point values to declutter it
\[\Large e^{2*0}\left(0+2\frac{dy}{dx}\right) +2(2) -2(0) \frac{dy}{dx}=0\]
\[\Large 2\frac{dy}{dx} +4=0\]