Given that $\sqrt{{{x}^{2}}+{{y}^{2}}}=3y$, find an expression of \(\frac{\mathrm{d}y}{\mathr

Question

Given that $\sqrt{{{x}^{2}}+{{y}^{2}}}=3y$, find an expression of $\frac{\mathrm{d}y}{\mathrm{d}x}$.

Accepted Answer

$\dfrac{\mathrm dy}{\mathrm dx}=\dfrac{x}{8y}$ for $x\ne0$; equivalently $\dfrac1{2\sqrt2}$ for $x>0$ and $-\dfrac1{2\sqrt2}$ for $x<0$. No derivative at $(0,0)$.

Techniques of Differentiation - Implicit Differentiation

Techniques of Differentiation - Implicit Differentiation

Solution:

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