Question

Differentiate the following with respect to x

y= e^x - 1
-------------
e ^x +1

Answer 1

Question :

Differentiate the following with respect to x

$\sf{ y = \frac{ {e}^{x - 1} }{ {e}^{x + 1} } }$

To find :

The value of y

Solution :

$\sf{ y = \frac{ {e}^{x - 1} }{ {e}^{x + 1} } }$

We know that,

$\sf \frac{ {x}^{a} }{ {x}^{b} } = {x}^{a - b}$

Now,

$\sf \: y = {e}^{x - 1} \div {e}^{x + 1}$

$\sf \: y = {e}^{x - 1 - (x + 1)}$

$\sf \: y = {e}^{x - 1 - x - 1}$

$\sf \: y = {e}^{ - 2}$

$\sf \: y = \frac{1}{ {e}^{2} }$

Final Answer :

$\ \boxed{ \sf \: so \: the \: value \: of \: y \: is \: \frac{1}{ {e}^{2} } }$

Answer 2

Step-by-step explanation:

$=e </p><p>x−1</p><p> ÷e </p><p>x+1</p><p> </p><p></p><p>\sf \: y = {e}^{x - 1 - (x + 1)}y=e </p><p>x−1−(x+1)</p><p> </p><p></p><p>\sf \: y = {e}^{x - 1 - x - 1}y=e </p><p>x−1−x−1</p><p> </p><p></p><p>\sf \: y = {e}^{ - 2}y=e </p><p>−2</p><p> </p><p></p><p>\sf \: y = \frac{1}{ {e}^{2} }y= </p><p>e </p><p>2</p><p> </p><p>1</p><p> </p><p> </p><p></p><p>Final$