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

[tachyon_man]

Homework Statement

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

Homework Equations

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?

 

[SammyS]

Homework Statement

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

Homework Equations

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?

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.

 

[tachyon_man]

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

 

[SammyS]

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

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

 

[tachyon_man]

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

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

 

[SammyS]

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

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

 

[tachyon_man]

Ok, thank you !