2(x^2)y + 2x + 4y – cos (PI*y) = 17. Find dy/dx using implicit differentiation.
This tests the students knowledge of differentiation rules as well as algebraic manipulation. Namely the product rule and implicit differentiation. Differentiate term by term and then isolate dy/dx using algebra to find the solution.
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A circle has equation: (x - 2)^2 + (y - 2)^2 = 16. It intersects the y-axis (y > 0) at point P and the x-axis (x < 0) at point Q. Find the equation of the line connecting P and Q and of the line perpendicular to PQ passing through the circle's centre.
Integrate dy/dx = 2x/(x^2-4)
differentiate: y^2 + 3xy + x + y = 8