Calculating $\\frac{dy}{dx}$ from an implicit polynomial function.
", "licence": "Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International"}, "statement": "If \\[ \\simplify{{a}y-{b}x^{n}={c}y^{m}}, \\]
\nfind $\\tfrac{dy}{dx}$.
", "advice": "As we have an equation involving the variables $x$ and $y$, but cannot rearrange the equation into the form $y=f(x)$, we need to use implicit differentiation to find $\\tfrac{dy}{dx}$.
\nDifferentiating $\\simplify{{a}y-{b}x^{n}={c}y^{m}}$ with respect to $x$:
\n\\[ \\simplify[all,!simplifyFractions]{{a}(d y/(d x)) - {b*n}x^{n-1} = {c*m}y^{m-1}}\\frac{dy}{dx}.\\]
\nRearranging this equation so that it is in terms of $\\tfrac{dy}{dx}$:
\n{advice}
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