If Sin-1×2-y2x2+y2=log a then dydx=

# If  then $\frac{\mathrm{dy}}{\mathrm{dx}}=$

1. A

$\frac{\mathrm{x}}{\mathrm{y}}$

2. B

$\frac{\mathrm{y}}{\mathrm{x}}$

3. C

$\frac{2{\mathrm{y}}^{2}}{{\left({\mathrm{x}}^{2}+{\mathrm{y}}^{2}\right)}^{2}}$

4. D

$\frac{2{x}^{2}}{\left({\mathrm{x}}^{2}+{\mathrm{y}}^{2}\right)}$

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### Solution:

The given equation is

it implies that $\frac{{x}^{2}-{y}^{2}}{{x}^{2}+{y}^{2}}=\mathrm{sin}\left(\mathrm{log}a\right)$

Differentiate both sides with respect to $x$

$\frac{\left({x}^{2}+{y}^{2}\right)\left(2x-2y\frac{dy}{dx}\right)-\left({x}^{2}-{y}^{2}\right)\left(2x+2y\frac{dy}{dx}\right)}{{\left({x}^{2}+{y}^{2}\right)}^{2}}=0$

Therefore, $\frac{dy}{dx}=\overline{)\frac{\mathbf{y}}{\mathbf{x}}}$

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