# Find equation of tangent line of tan(xy^2)=(2xy)/pi (implicit diff.)

1. Oct 28, 2012

### tachyon_man

1. The problem statement, all variables and given/known data

Find the equation of the tangent line of tan(xy2)=(2xy)/$\pi$ at (-$\pi$,1/2)

2. Relevant equations

3. The attempt at a solution

I managed to get the equation into its dy/dx form and for the slope to be (1-.5pi)/(2pi-2pi2)
This seems far to complicated to be correct though.. can someone confirm this?

Last edited: Oct 28, 2012
2. Oct 28, 2012

### SammyS

Staff Emeritus
Please show your result for implicit differentiation prior to substituting for the given point. I get something different for y' at that point, but it's similarly complicated.

3. Oct 28, 2012

### tachyon_man

Here's what I got, dy/dx = [y2(pi)sec2(xy2)-2y]/[(2x)(1-y(pi)sec2(xy2)]

4. Oct 28, 2012

### SammyS

Staff Emeritus
I checked your (implicit) differentiation and the value of the derivative at (-π, 1/2) with WolframAlpha, and it agrees with your results totally.

5. Oct 28, 2012

### tachyon_man

That's always good to hear :p So my slope I found is most likely right? Even tho its a mess to look at?

6. Oct 28, 2012

### SammyS

Staff Emeritus
Yes, I'm quite sure that it's correct.

Last edited: Oct 28, 2012
7. Oct 28, 2012

### tachyon_man

Ok, thank you !