y=(1+1/x)^x (y等于1加x分之1的x次方)求导!要过程!

y=(1+1/x)^x (y等于1加x分之1的x次方)求导!要过程!

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y=(1+1/x)^x，
即y=e^ [x*ln(1+1/x)]，
所以哗桐
y'= e^ [x*ln(1+1/睁销x)] * [x*ln(1+1/x)] '
而
[x*ln(1+1/x)] '
= x' * ln(1+1/x) + x* [ln(1+1/x)] '
= ln(1+1/x) + x* [-(1/x^2) / (1+1/x)]
= ln(1+1/x) - 1/(x+1)
故
y'= e^ [x*ln(1+1/x)] * [x*ln(1+1/x)] '
= e^ [x*ln(1+1/x)] * [ln(1+1/x) - 1/(x+1)]
= (1+1/x)^x * [ln(1+1/乱早坦x) - 1/(x+1)]

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1/y = (2^x+1)/悉蚂岩2^x = 1 + 2^(-x) >物凳1
2^(-x) = 1/y -1
x = -log2 (1/y -1) (0<y<睁御1)

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