3. Find the equation of the tangent line to the curve 2x^3 + y^2 = xy at the point (−1, 1).
4. Use implicit differentiation to find y' for sin(xy^2 ) − x^3 = 4x + 2y.
5. Use logarithmic differentiation to find y' for y = e^4x cos(2x) / (x−1)^4 .
6. Show that d/dx (tan (x)) = sec^2 (x) using only your knowledge of the derivatives of sine/cosine with derivative rules.
7. Use implicit differentiation to show that d/dx (tan−1 (x)) = 1 / 1+x^2 .
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