What is at x = 1 equal to?

Question

Question

Directions: Read the following information and answer the two items that follow:

Consider the equation x^y = e^x-y

This question was previously asked in

NDA (Held On: 17 Nov 2019) Maths Previous Year paper

Attempt in App

Answer 1

Concept:

Calculation:

Given: x^y = e^x-y

By applying ln both the sides we get

⇒ y × ln x = ln (e^x-y) = x – y

⇒ y × ln x = x – y

⇒ x = y × (1 + ln x) ------(1)

Now by differentiating both the sides with respect to x we get,

Now by using equation (1), we get

So,