Determine the directional derivative of the function f(x, y) = (5x³ 7y±+15xy)/T in the direction given by the curve r(t) = (3n cos(2t), 5 sin(2t)) at the point given by t=a.

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A: To find the derivative of the given function.

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Q: Consider the equation: y²³ - 3xy + x 5 = 1 a) Calculate dy using implicit differentiation. dx b)…

A: y2 -3xy+ x5 = 1Finding dy/dx using implicit differentiation 2y dy/dx - 3x dy/dx - 3y + 5 x4 = 0dy/dx…