Not all equations can be written like y = f(x), so taking the derivative can be tricky. Save the mess and do it directly with implicit differentiation.

If \[\frac { x ( x - 6y) } { 5 - 4 y^ 2 } = 1, \] what is \(\displaystyle \frac{dy}{dx}?\)

If \( \frac{ 3 x ^2 + 7 xy^2 } { 8 + 5 y^3 } = 1 \), what is \(\displaystyle \frac{dy}{dx}?\)

If \[\frac{6x-y^3}{y+x^2}=x+4, \] what is \(\displaystyle \frac{dy}{dx}?\)

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