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Question

Mathematics Question on Statistics

If y=sin⁡−1(3−x)y= \sin^{-1} (3^{-x}), then dydx=\frac{dy}{dx} =

A

−log⁡332x−1-\frac{\log 3}{\sqrt{3^{2x}-1}}

B

3xlog⁡332x−1\frac{3^{x}\log 3}{\sqrt{3^{2x}-1}}

C

−3xlog⁡332x−1\frac{- 3^{x}\log 3}{\sqrt{3^{2x}-1}}

D

log⁡33x32x−1\frac{\log 3}{3^{x} \sqrt{3^{2x}-1}}

Answer

−log⁡332x−1-\frac{\log 3}{\sqrt{3^{2x}-1}}

Explanation

Solution

We have , y=sin⁡−1(3−x)dydx=11−3−2x.(−1).3−xlog⁡3y= \sin^{-1} (3^{-x}) \frac{dy}{dx} = \frac{1}{\sqrt{1-3^{-2x}}}.\left(-1\right).3^{-x} \log 3
=−3−xlog⁡332x−132x=log⁡332x−1=\frac{-3^{-x}\log 3}{\sqrt{\frac{3^{2x} -1}{3^{2x}}}} = \frac{\log 3}{\sqrt{3^{2x} -1}}