Use implicit differentiation to find dy/dx of: 2(x^2)y + 2x + 4y - cos((pi)y) = 17
Tackle this problem one part at a time: First differentiate 2x2y using the product rule, showing dy/dx(2x2y) = 4xy + 2x2(dy/dx). After this, the remainder of the question is easier, as there are no more mixes of x and y. dy/dx(2x + 4y - cos((pi)y)) = 2 + 4(dy/dx) + (pi)(dy/dx)sin((pi)y) Also, dy/dx(17) = 0 Hence the equation you get is: 4xy + 2x2(dy/dx) + 2 + 4(dy/dx) + (pi)(dy/dx)sin((pi)y) = 0 Rearranging, you can see: dy/dx = (-2 - 4xy)/(2x2 + 4 + (pi)sin((pi)y))
NE
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