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Sauron [17]
2 years ago
13

Y is a differentiable function of x. Choose the alternative that is the derivative dy / dx.

Mathematics
1 answer:
murzikaleks [220]2 years ago
3 0

Differentiating both sides of

x^3-y^3=1

with respect to <em>x</em> yields (using the chain rule)

3x^2 - 3y^2 \dfrac{\mathrm dy}{\mathrm dx} = 0

Solve for d<em>y</em>/d<em>x</em> :

3x^2 - 3y^2 \dfrac{\mathrm dy}{\mathrm dx} = 0 \\\\ 3y^2\dfrac{\mathrm dy}{\mathrm dx} = 3x^2 \\\\ \dfrac{\mathrm dy}{\mathrm dx} = \dfrac{3x^2}{3y^2} = \dfrac{x^2}{y^2}

The answer is then D.

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