Find the derivative of (2^x-e^x)/(2^x+e^x)
just plug and chug, using the quotient rule
(2^x ln2 - e^x)(2^x+e^x) - (2^x-e^x)(2^x ln2 + e^x)
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(2^x+e^x)^2
You can simplify that to
2^(x+1) e^x (ln2 - 1) / (2^x+e^x)^2