How do you differentiate $y=sqrt(2-e^x)$ ?

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Answer 1 · 2017-04-04T15:32:07

Use the chain rule:
$(d(f(g(x))))/dx = (df(g))/(dg)(d(g(x)))/dx$

Let $g(x) = 2 - e^x$ then it follows that:

$(d(g(x)))/dx= -e^x$

$f(g) = sqrt(g)$

and

$(df(g))/(dg) = 1/(2sqrtg)$

Substituting this into the chain rule:

$(d(sqrt(2-e^x)))/dx =1/(2sqrtg)-e^x$

$(d(sqrt(2-e^x)))/dx =-e^x/(2sqrtg)$

Reverse the substitution for g:

$(d(sqrt(2-e^x)))/dx =-e^x/(2sqrt(2-e^x))$

How do you differentiate y=sqrt(2-e^x)y=sqrt(2-e^x)?