Question

Use implicit differentiation to find y': 2(x^2 + y^2)^2 = 25(x^2 - y^2)

Answer 1

\[\frac {d}{dx} \left[ 2(x^2 + y^2)^2 \right] = \frac {d}{dx} \left[ 25x^2 -25 y^2 \right]\]\[4(x^2 + y^2) \times \frac {d}{dx} \left[ x^2 + y^2 \right] = 50x - 50y y'\]\[4(x^2 + y^2) \times ( 2x + 2yy') = 50x - 50y y'\]Now just rearrange and solve for y'...