# Check my answer for implicit function problem?

1. May 7, 2013

### asdf12312

1. The problem statement, all variables and given/known data
Use the IMPLICIT FUNCTION THEOREM (and not implicit diﬀerentiation) to ﬁnd dy/dx at the point (1,1) when
y^5 + x^2*y^3 − y*e^(x^2) = 1.

2. Relevant equations
f(x,y)=0
dy/dx = - [f(x)/f(y)] = -[d/dx(f(x,y) / d/dy(f(x,y)]

3. The attempt at a solution
solving for f(x,y), i brought the 1 to the left side so the equation equaled 0, i.e y^5 + x^2*y^3 − y*e^(x^2)-1=0

then d/dx of the function I got 2xy^3 - 2xye^(x^2)
d/dy = 5y^4 + 3x^2y^2 - e^(x^2)

so dy/dx was just -[d/dx / d/dy] = -[2xy^3 - 2xye^(x^2) / 5y^4 + 3x^2y^2 - e^(x^2)]
for the point (1,1) i just plugged in x and y into the above equation, and got 0.65 as my answer.

Last edited: May 7, 2013
2. May 7, 2013

### janhaa

I got:

dy/dx = -1.41

3. May 7, 2013

### asdf12312

can you show your work? did you get the same equation for dy/dx as me? if i got mine wrong it was probably the ye^(x^2) part, since i was kinda confused how to work it. for d/dx, i got 2xye^(x^2), and for d/dy i got e^(x^2).

4. May 7, 2013

### janhaa

sorry, my mistake, I also got

dy/dx = 0,65