Question

find the derivative of f(x) = X+1/x-1​

Answer 1

Answer:

f'(x)=x-X-2

---------

(x-1)^2

Step-by-step explanation:

f'(x)=(x-1)*1-(X+1)*1

-------------------

(x-1)^2

=x-X-2

---------

(x-1)^2

Answer 2

Answer:

your solution is as follows

pls mark it as brainliest

Step-by-step explanation:

$to \: find : \frac{d}{dx} \: f(x) = \frac{x + 1}{x - 1} \\ \\ we \: know \: that \\ according \: to \: quotient \: rule \\ of \: differentiation \\ \\ \frac{d}{dx} ( \frac{u}{v} ) = \frac{v. \frac{d}{dx} (u) - u. \frac{d}{dx} (v)}{v {}^{2} } \\ \\ = \frac{(x - 1). \frac{d}{dx} (x + 1) - (x + 1). \frac{d}{dx} (x - 1)}{(x - 1) {}^{2} } \\ \\ = \frac{(x - 1).1 - (x + 1).1}{(x - 1) {}^{2} } \\ \\ = \frac{x - 1 - x - 1}{(x - 1) {}^{2} } \\ \\ = - \frac{2}{(x - 1) {}^{2} }$