If [ $$.$$ ] denotes the greatest integer function and y $$=$$ tan π7x $$-$$ 4π41 $$+$$ 3x $$-$$ 22, then dydx $$=$$

sec 2 π 7 x - 4 π 4 × 28 7 x - 4 π 3 1 + 3 x - 2 π 2 2

Questions

If [ . ] denotes the greatest integer function and $y = \frac{\tan π [{(7 x - 4 π)}^{4}]}{1 + {[3 x - 2]}^{2}}$ , then $\frac{dy}{dx} =$

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\sec^{2} π

\frac{\sec^{2} π [{(7 x - 4 π)}^{4}] \times 28 {(7 x - 4 π)}^{3}}{{(1 + {[3 x - 2 π]}^{2})}^{2}}

secπ \tan \frac{π}{4}

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detailed solution

Correct option is D

The given function is $y = \frac{\tan π [{(7 x - 4 π)}^{4}]}{1 + {[3 x - 2]}^{2}}$

Since $\tan (n π)$ is zero for any value of $n$ , the above function is zero

Hence, $\frac{d y}{d x} = 0$

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If [ . ] denotes the greatest integer function and y = tan π7x - 4π41 + 3x - 22, then dydx =