Question

Differentiate

$y = \sqrt{1 + e {}^{x} }$
with respect to x
​

Answer 1

$GOOD \: \: MORNING \: \\ \\ y = \sqrt{1 + e {}^{x} } \\ \\ Differentiate \: \: both \: sides \: w.r.t \: x \: w e \: have \\ \\ dy \div dx \: = (1 \div 2 \sqrt{(1 + e {}^{x} )} ) \times e {}^{x} \\ \\ dy \div dx \: = e {}^{x} \times (1 \div 2 \sqrt{(1 + e {}^{x}) }$

Answer 2

Hi

Solution :- y = (1 + e^x)^1/2

Diffrentiating (1 + e^x) with respect to x

y = (1+e^x)^1/2

y =

dy/dx = 1/2 {1 + e^x}^(1-1/2)* e^x

Note:- 1st of all we diffrenciat (1 + e^x)^½ function then diffrenciate ( 1+ e^x) functions of function

diffrentiation of (1 + e^x)^½ = 1/2( 1+ e^x) ^-½ then diffrenciate function of function (1+ e^x) = e^x

after substituting value we get .

dy/dx = 1/2( 1+ e^x)-½* ex

Answer ✔✔

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Hope it helps you !!!

@Raj❤