Function and derivativeCalculateĀ the derivative of the function f(x) = e^[x/(x+2)] .

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justaguide's profile pic

justaguide | College Teacher | (Level 2) Distinguished Educator

Posted on

We have to find the derivative of f(x) = e^[x/(x+2)]

We use the chain rule here:

f'(x) = e^[x/(x + 2)]*[(1/(x + 2) - x/(x + 2)^2]

=> e^[x/(x + 2)]*[((x + 2 - x)/(x + 2)^2]

=> e^[x/(x + 2)]*[(2/(x + 2)^2]

The required derivative of f(x) = e^[x/(x+2)] is e^[x/(x + 2)]*[(2/(x + 2)^2]

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giorgiana1976 | College Teacher | (Level 3) Valedictorian

Posted on

We'll apply chain rule to determine the derivative of the function:

f'(x) = e^[x/(x+2)]*[x/(x+2)]'

Since we have to differentiate a fraction, we'll apply quotient rule:

(u/v)' = (u'v - uv')/v^2

u = x => u' = 1

v = (x+2) => v' = 1

[x/(x+2)]' = [(x+2) - x]/(x+2)^2

We'll eliminate like terms:

[x/(x+2)]' = 2/(x+2)^2

The derivative of the function is:

f'(x) = [2/(x+2)^2]*e^[x/(x+2)]

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