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Back to Derivatives of functions given implicitly

Activity 2.7.4

Avg difficulty 2.5

For each of the following curves, use implicit differentiation to find dy/dxdy/dx and determine the equation of the tangent line at the given point.

  1. x3−y3=6xyx^3 - y^3 = 6xy,  (−3,3)(-3,3)

  2. sin⁡(y)+y=x3+x\sin(y) + y = x^3 + x,  (0,0)(0,0)

  3. 3xe−xy=y23x e^{-xy} = y^2,  (0.619061,1)(0.619061,1)

Boelkins, Active Calculus, §2.7 Derivatives of functions given implicitly, Activity 2.7.4

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Adapted from Active Calculus © 2012–2025 Matthew Boelkins. Licensed under CC BY-SA 4.0. Source: Active Calculus. Imported at revision dc86ba3.