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What is the derivative of f(x) = e^2x - 2/(1 - e^x)

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torrip996 | Student, Grade 10 | Salutatorian

Posted September 11, 2013 at 4:11 PM via web

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What is the derivative of f(x) = e^2x - 2/(1 - e^x)

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justaguide | College Teacher | (Level 2) Distinguished Educator

Posted September 11, 2013 at 4:18 PM (Answer #1)

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The derivative of `f(x) = (e^(2x) - 2)/(1 - e^x)` has to be determined. Use the quotient rule.

f'(x) = `((e^(2x) - 2)'(1 - e^x) - (e^(2x) - 2)(1 - e^x)')/(1 - e^x)^2`

= `(2*e^(2x)(1 - e^x) - (e^(2x) - 2)(- e^x))/(1 - e^x)^2`

= `(2*e^(2x) - 2*e^(3x) + e^(3x) - 2e^x)/(1 - e^x)^2`

= `(2*e^(2x) - e^(3x) - 2e^x)/(1 - e^x)^2`

= `(e^x*(2e^x - e^(2x) - 2))/(1 - e^x)^2`

The derivative of `f(x) = (e^(2x) - 2)/(1 - e^x) ` is `f'(x) = (e^x*(2e^x - e^(2x) - 2))/(1 - e^x)^2`

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