If x=ey+ey+ey……..∞ and dydx=1−kxx, then k=?

# If $x={e}^{y+{e}^{y+{e}^{y........\infty }}}$ and

Fill Out the Form for Expert Academic Guidance!l

+91

Live ClassesBooksTest SeriesSelf Learning

Verify OTP Code (required)

I agree to the terms and conditions and privacy policy.

### Solution:

Given $x={e}^{y+x}$

Take logarithm on both sides

$\begin{array}{l}\mathrm{log}x=\mathrm{log}{e}^{y+x}\\ \mathrm{log}x=\left(y+x\right)\mathrm{log}e\\ \mathrm{log}x=y+x\end{array}$

Differentiate both sides with respect to $x$

$\frac{1}{x}=\frac{dy}{dx}+1⇒\frac{dy}{dx}=\frac{1}{x}-1⇒\frac{dy}{dx}=\frac{1-x}{x}$

Therefore, $k=1$

## Related content

 Area of Square Area of Isosceles Triangle Pythagoras Theorem Triangle Formulae Perimeter of Triangle Formula Area Formulae Volume of Cone Formula Matrices and Determinants_mathematics Critical Points Solved Examples Type of relations_mathematics

Talk to our academic expert!

+91

Live ClassesBooksTest SeriesSelf Learning

Verify OTP Code (required)

I agree to the terms and conditions and privacy policy.