Y= x+1/x-1 - найти производную

Question

Y= x+1/x-1 - найти производную

Answer 1

У' = ((x+1)'*(x-1) - (x-1)'*(x+1))/(x-1)² 
y'=(1*(x-1)-1(x+1))/(x-1)²
y'=(x-1-x-1)/(x-1)²
y'=-2/(x-1)²

Comments

(U/V)'=(U'V-UV')/V^2 ?

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d/dx[f(x)/g(x)] = g(x)d/dx[f(x)]-f(x)d/dx[g(x)] / g(x)^2

f(x) = x+1
g(x) = x-1

(x-1)d/dx[x+1]

-(x+1)[x-1]/ (x-1)^2

x-1-(x+1) / (x-1)^2

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- 2/(x-1)^2

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Я вот так сделал