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Practice Problems for 3/6

  1. In your own words, explain the difference between an explicit and implicit relationship.

  2. Use implicit differentiation to find \(\frac{dy}{dx}\) for each of the following equations.
    1. \(xy=7\)
    2. \(\sin(x+y)=y^2\cos x\)
    3. \(e^{xy}=e^{4x}-e^y\)

  3. Explain why and where you used the chain rule in part b of #2.

  4. The folium of Descarte (pictured below) is given by the equation \(x^3+y^3=6xy\)
    1. Find the equation for the tangent line to the folium at the point (3,3).
    2. Find the equation for the normal line to the folium at the point (3,3)