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y² + 2xy dy/dx = 3cos(3x) + 1/y - x/y² dy/dx                   thereforedy/dx = (3cos(3x) + 1/y - y²​​​​​​) / (2xy + x/y²)

When I am expanding brackets I use the acronym FOIL and simplify. You begin by multiply the first term (F) in each bracket, followed by multiplying the outside terms (O), then the inside terms (I) and fin...

cos(2x) = 2cos²(x) - 1 This is the identity. Therefore we can substitute in 2[cos²(x)] to be 2 multiplied by (1/4)².Therefore cos(2x) = 2(1/4)(1/4) - 1 = 2/16 - 1 = 2/16 -...