The curve C has equation ye^(-2x) = 2x + y^2. Find dy/dx in terms of x and y.
The curve's equation is presented as an implicit function. Therefore we must use implicit differentiation to solve this problem. To do this, we differentiate both sides of the equation with respect to x, applying the chain rule where a y variable appears, and then rearrange to give dy/dx. The equation given in the question differentiates implicitly to e-2x(dy/dx) - 2ye-2x = 2 + 2y(dy/dx). This can be rearranged to dy/dx = (2 + 2ye-2x )/ (e-2x- 2y)
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