IIT JEE , AIEEE Forum - Mathematics , Differential Calculus

mujtaba4iit

See the solution for 4.

$\frac{x^2- y^2}{x^2+y^2}\,=cos{(log a)}=k\,\,\,\,(say)<br/>\\ By \,componendo-dividendo\\\,\frac{x^2}{-y^2}= \frac{k+1}{k-1}\\\,\frac{x^2}{y^2}= \frac{1+k}{1-k}\\\,\frac{x}{y}= \sqrt\frac{1+k}{1-k}\\\,Now\,differentiating\, wrt\,x\\\,\frac{d}{dx}{(\frac{x}{y})}=0\\\, y-x{\frac{dy}{dx}}=0\\\,y=x{\frac{dy}{dx}}\\\,so\, {\frac{dy}{dx}}=\frac{y}{x}$

Plz nudge me if u dont understand any step.

This sum can be done in different ways also, try by some other method.

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