The discussion revolves around finding the equation of the tangent line for the implicit function defined by tan(xy²) = (2xy)/π at the point (-π, 1/2). The subject area includes implicit differentiation and calculus concepts related to tangent lines.
Some participants have shared their expressions for dy/dx and noted agreement with computational tools. There is a sense of validation regarding the results, but the complexity of the expressions remains a point of discussion. No explicit consensus has been reached on the simplicity or clarity of the solutions presented.
Participants are working under the constraints of implicit differentiation and are focused on confirming their results at a specific point. There is an emphasis on the accuracy of the differentiation process and the resulting expressions.
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.kylem1994 said: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?
I checked your (implicit) differentiation and the value of the derivative at (-π, 1/2) with WolframAlpha, and it agrees with your results totally.kylem1994 said:Here's what I got, dy/dx = [y2(pi)sec2(xy2)-2y]/[(2x)(1-y(pi)sec2(xy2)]
SammyS said:I checked your (implicit) differentiation and the value of the derivative at (-π, 1/2) with WolframAlpha, and it agrees with your results totally.
Yes, I'm quite sure that it's correct.kylem1994 said:That's always good to hear :p So my slope I found is most likely right? Even tho its a mess to look at?