What is the derivative of {e}^{e^{x}} with respect to e^{x}?

Correct Answer is : eex{e}^{e^{x}}eex

Correct Answer is : eex{e}^{e^{x}}eex

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UPSC NDA 2 2021 Mathematics Solved Paper

Question : 94 of 120

Marks: +1, -0

\mathrm{e}^{e^{x}}

e^{x}

Solution:

Concept:

To find the derivative of one function with respect to another, differentiate each with respect to the same independent variable and then divide.

Explanation:

Let

y = e^{e^{x}}

and

u = e^{x}

We need

\frac{dy}{du}

First, differentiate

y

with respect to

x

\frac{dy}{dx} = e^{e^{x}} \cdot e^{x}

(using chain rule).

Next, differentiate

u

with respect to

x

\frac{du}{dx} = e^{x}

Now,

\frac{dy}{du} = \frac{dy/dx}{du/dx} = \frac{e^{e^{x}} \cdot e^{x}}{e^{x}} = e^{e^{x}}

Answer:

e^{e^{x}}

(Option A)

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