Find \(\rm \frac{dy}{dx}\), if y = elog (log x)1. \(\rm \frac 1 x\)2.

1.	Find \(\rm \frac{dy}{dx}\), if y = elog (log x)1. \(\rm \frac 1 x\)2. \(\rm \frac {1}{\log x}\)3. elog (log x)4. None of these
Answer» Correct Answer - Option 1 : \(\rm \frac 1 x\) Concept: \(\rm \frac{d(\log x)}{dx} = \frac 1 x\) Calculation: Given: y = e^{log (log x)} To Find: \(\rm \frac{dy}{dx}\) As we know that, e^{log x} = x ∴ e^{log (log x)} = log x Now, y = log x Differentiating with respect to x, we get \(\rm \frac{dy}{dx}=\rm \frac{d(\log x)}{dx} = \frac 1 x\)

Find \(\rm \frac{dy}{dx}\), if y = elog (log x)1. \(\rm \frac 1 x\)2. \(\rm \frac {1}{\log x}\)3. elog (log x)4. None of these

Answer» Correct Answer - Option 1 : \(\rm \frac 1 x\)

Concept:

\(\rm \frac{d(\log x)}{dx} = \frac 1 x\)

Calculation:

Given: y = e^{log (log x)}

To Find: \(\rm \frac{dy}{dx}\)

As we know that, e^{log x} = x

∴ e^{log (log x)} = log x

Now, y = log x

Differentiating with respect to x, we get

\(\rm \frac{dy}{dx}=\rm \frac{d(\log x)}{dx} = \frac 1 x\)

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Find \(\rm \frac{dy}{dx}\), if y = elog (log x)1. \(\rm \frac 1 x\)2. \(\rm \frac {1}{\log x}\)3. elog (log x)4. None of these

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