Techniques of Differentiation - Implicit Differentiation
Techniques of Differentiation - Implicit Differentiation
Given that \({{x}^{2}}={{\left( 4{{x}^{2}}{{y}^{3}}+1 \right)}^{2}}\), find an expression of \(\frac{{\mathrm{d}y}}{\mathrm{d}x}\).
Solution:
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Answer:\(\dfrac{\mathrm dy}{\mathrm dx}=\dfrac{1-4x^2y^3}{12x^3y^2}\), for \(x\ne0,\ y\ne0\).
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