If y=2x 32x 5-x 7-x then dydx=

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$If y = 2^{x} 3^{2 x} 5^{- x} 7^{- x} then \frac{dy}{dx} =$

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$\frac{2^{x} . 3^{2 x}}{5^{x} 7^{x}} \log \frac{35}{18}$

$\frac{2^{x} . 3^{2 x}}{5^{x} 7^{x}} \log \frac{14}{45}$

$\frac{2^{x} . 3^{2 x}}{5^{x} 7^{x}} \log \frac{18}{35}$

$\frac{2^{x} . 3^{2 x}}{5^{x} 7^{x}} \log \frac{45}{14}$

answer is A.

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Detailed Solution

$y = 2^{x} . 3^{2 x} . 5^{- x} . 7^{- x} y = {(\frac{2.9}{5.7})}^{x} = {(\frac{18}{35})}^{x} \frac{dy}{dx} = {(\frac{2.9}{5.7})}^{x} \log (\frac{18}{35}) = \frac{2^{x} . 3^{2 x}}{5^{x} . 7^{x}} \log (\frac{18}{35})$

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