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In questions where we have a function of x and y equal to a constant, we need to find dy/dx indirectly.We use the formula (df/dx) + (df/dy)(dy/dx) = 0So all we do is differentiate each term in the functio...

Student uses the definition of area [A = 1/2 integral r(theta)^2 d theta], and proceeds using standard integration techniques to give a quadratic solvable for alpha. [alpha^2 = 25] Thus, alpha = 5.

2x²y + 2x + 4y - cos(πy) = 45Applying implicit differentiation:4xy + 2x²(dy/dx) + 2 + 4(dy/dx) + πsin(πy)(dy/dx) = 0Moving all (dy/dx) terms to one side:2x² (dy/dx) + 4(dy...