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Question Number 98895 by bramlex last updated on 17/Jun/20

$$Is\frac{dy}{dx}if{y}^3+x^3-2x=1?$$

Answered by bramlex last updated on 17/Jun/20

Answered by mathmax by abdo last updated on 17/Jun/20

$${\mathrm{y}}^3+{\mathrm{x}}^3-2\mathrm{x}=1\Rightarrow {\mathrm{y}}^3=-{\mathrm{x}}^3+2\mathrm{x}+1\Rightarrow \mathrm{y}={(-{\mathrm{x}}^3+2\mathrm{x}+1)}^{\frac{1}{3}}\Rightarrow$$$$\frac{\mathrm{dy}}{\mathrm{dx}}=\frac{1}{3}{(-{3\mathrm{x}}^2+2)}^{-\frac{2}{3}}=\frac{1}{3\left({}^3\sqrt{{(-{3\mathrm{x}}^2+2)}^2}\right)}$$

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