Expert Answer to "Find the derivative of the following functions f(x)=2x2x+1" - Plainmath

a2linetagadaW

Answered question

2021-10-13

Find the derivative of the following functions

f (x) = \frac{2^{x}}{2^{x} + 1}

Answer & Explanation

Luvottoq

Skilled2021-10-14Added 95 answers

Given
The given function is

f (x) = \frac{2^{x}}{2^{x} + 1}

find the derivative

f^{'} (x) = \frac{d}{d x} (\frac{2^{x}}{2^{x} + 1})

= \frac{(2^{x} + 1) \frac{d}{d x} (2^{x}) - 2^{x} \frac{d}{d x} (2^{x} + 1)}{{(2^{x} + 1)}^{2}}

= \frac{(2^{x} + 1) (2^{x} \ln 2) - 2^{x} (2^{x} \ln 2)}{{(2^{x} + 1)}^{2}}

= \frac{2^{x} (2^{x} \ln 2) + (2^{x} \ln 2) - 2^{x} (2^{x} \ln 2)}{{(2^{x} + 1)}^{2}}

= \frac{2^{x} \ln 2}{{(2^{x} + 1)}^{2}}

Jeffrey Jordon

Expert2022-03-24Added 2605 answers

Answer is given below (on video)

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