Question

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If cos^-1(y/b)=log(x/n)^n ,then find the innate differentiation...

Answer 1

Given,

$\cos^{-1}(\frac{y}{b})=\log(\frac{x}{n})^{n}\\\;\\\cos^{-1}(\frac{y}{b})=n\log\frac{x}{n}\\\;\\\cos^{-1}(\frac{y}{b})=n(\log x-\log n)\\\;\\\text{diff. both sides w.r.t. x}\\\;\\(\frac{1}{\sqrt{1-\frac{y^{2}}{b^{2}}}}).\frac{1}{b}\frac{dy}{dx}=n(\frac{1}{x}-0})\\\;\\(\frac{b}{\sqrt{b^{2}-y^{2}}}).\frac{1}{b}.\frac{dy}{dx}=\frac{n}{x}\\\;\\\frac{1}{\sqrt{b^{2}-y^{2}}}.\frac{dy}{dx}=\frac{n}{x}\\\;\\\frac{dy}{dx}=\frac{n\sqrt{b^{2}-y^{2}}}{x}$

Answer 2

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