frac{d}{d x}left(e^{log _e sqrt{1+tan ^2 x}}r | vedclass

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(C) We know that $e^{\log _e f(x)} = f(x)$.Given expression is $\frac{d}{d x}\left(e^{\log _e \sqrt{1+	an ^2 x}}ight)$.Using the property,this simp

Vedclass · Accepted Answer

$\sec (x) \cdot 	an (x)$

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(C) We know that $e^{\log _e f(x)} = f(x)$.Given expression is $\frac{d}{d x}\left(e^{\log _e \sqrt{1+	an ^2 x}}ight)$.Using the property,this simplifies to $\frac{d}{d x}\left(\sqrt{1+	an ^2 x}ight)$.Since $1+	an ^2 x = \sec ^2 x$,we have $\sqrt{1+	an ^2 x} = \sqrt{\sec ^2 x} = |\sec x|$.Assuming $\sec x > 0$,we differentiate $\sec x$ with respect to $x$.$\frac{d}{d x}(\sec x) = \sec x 	an x$.

$\frac{d}{d x}\left(e^{\log _e \sqrt{1+\tan ^2 x}}\right) =$

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