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Question Number 70582 by Raphael last updated on 05/Oct/19

$$\mathrm{Given}\mathrm{that}\mathrm{y}=\frac{4}{\sqrt{({\mathrm{x}}^3+1)}}\mathrm{show}\mathrm{that}2({\mathrm{x}}^3+1)\frac{\mathrm{dy}}{\mathrm{dx}}=-{3\mathrm{x}}^2\mathrm{y}.$$

Commented by kaivan.ahmadi last updated on 05/Oct/19

$$2(x^3+1)\times \frac{-\frac{4\times 3x^2}{2\sqrt{x^3+1}}}{x^3+1}=2\times \frac{-2\times 3x^2}{\sqrt{x^3+1}}=$$$$-3x^2\times \frac{4}{\sqrt{x^3+1}}=-3x^{2}y$$

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