Techniques of Differentiation - Derivatives of Exponential Functions

Techniques of Differentiation - Derivatives of Exponential Functions

It is given that \(y={{\left( 2-{{\text{e}}^{x}} \right)}^{\frac{1}{3}}}\). Show that \(3{{y}^{2}}\frac{\mathrm{d}y}{\mathrm{d}x}={{y}^{3}}-2\).

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Answer:\(3y^2\dfrac{\mathrm dy}{\mathrm dx}=y^3-2\), for \(x\ne\ln2\).

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