# 2.6

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1. Consider the follwing equation. 7x^2 – y^2 = 3
(a) Find y’ by implicit differentiation
(b) Solve the equation explicitly for y and differentiate to get y’ in terms of x.
2. Find dy/dx by implicit differentiation. x^8 + y^3 = 9
3. Find dy/dx by implicit differentiation. 6x^3 +x^2y –xy^3 = 7
4. Find dy/dx by implicit differentiation. 2x^2 + 5xy – y^2 = 9
5. Find dy/dx by implicit differentiation. Y cos x = 4x^2 + 3y^2
6. Find dy/dx by implicit differentiation. 9 cos x sin y = 6
7. Find dy/dx by implicit differentiation. Sqrt(xy) = 3 + x^2y
8. Use the implicit differentiation to find an equation of the tangent line to the curve at the given point. 8x^2 +xy + 8y^2 = 17, (1, 1) (ellipse)
9. Use the implicit differentiation to find an equation of the tangent line to the curve at the given point. X^2 + y^2 = (5x^2 + 4y^2 – x)^2
(0, 0.25) (cardioid)
10. Use the implicit differentiation to find an equation of the tangent line to the curve at the given point. Y^2(y^2 -4) = x^2(x^2 -5) (0, -2) (devil’s curve)
11. Find the points on the lemniscate where the tangent is horizontal.
2(x^2 + y^2)^2 = 25(x^2 – y^2)
12. Find equations of both the tangent lines to the ellipse x^2 + 4y^2 = 36 that pass through the point (12, 3).