On considre la courbe d'quation

x^3+y^3=4xy+1.

Le long de cette courbe (sauf en quelques points),yest une fonction implicite dex.

a)Dterminer la drivedy/dxen fonction dexet dey.

b)En dduire l'quation de la tangente la courbex3+y3=4xy+1au point(0,1). Exprimer votre rponse sous la formey=ax+b.

English:

We consider the curve of equation x^3+y^3=4xy+1. Along this curve (except at a few points), y is an implicit function of x. a) Determine the derivative dy/dx as a function of x and y. b) Deduce the equation of the tangent to the curve x3+y3=4xy+1 at point (0,1). Express your answer as y=ax+b.