If x=e^{y+e^{y+e^{y+ldots}}},then frac{d y}{d | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(A) Given that,$x = e^{y+e^{y+e^{y+\ldots}}}$.Since the exponent repeats infinitely,we can write $x = e^{y+x}$.Taking the natural logarithm on both si

Vedclass · Accepted Answer

$\frac{1-x}{x}$

Vedclass · Answer

(A) Given that,$x = e^{y+e^{y+e^{y+\ldots}}}$.Since the exponent repeats infinitely,we can write $x = e^{y+x}$.Taking the natural logarithm on both sides,we get $\log_e x = y+x$.Rearranging for $y$,we have $y = \log_e x - x$.Differentiating both sides with respect to $x$,we get $\frac{dy}{dx} = \frac{d}{dx}(\log_e x) - \frac{d}{dx}(x)$.Thus,$\frac{dy}{dx} = \frac{1}{x} - 1 = \frac{1-x}{x}$.Therefore,option $(A)$ is correct.

If $x=e^{y+e^{y+e^{y+\ldots}}}$,then $\frac{d y}{d x}=$

Similar Questions

Two spherical conductors each of capacity $C$ are charged to potentials $V$ and $-V$. These are then connected by means of a fine conducting wire. The loss of energy will be

An increase in $CO_2$ concentration in the atmosphere will result in

In $Fe(CO)_5$,the $Fe-C$ bond possesses

On heating a mixture of $SO_2Cl_2$ and $CO$,two equilibria are simultaneously established:
$SO_2Cl_{2(g)} \rightleftharpoons SO_{2(g)} + Cl_{2(g)}$
$CO_{(g)} + Cl_{2(g)} \rightleftharpoons COCl_{2(g)}$
On adding more $SO_2$ at equilibrium,what will happen?

In the electrolytic extraction of $Al$,molten cryolite is used because it .......

Vedclass Test Series

Exam Paper Generator

Online Exam Module