What is the derivative of x^2-1-((x+1/(x-1))) ?

The derivative of x^2-1-((x+1/(x-1))) is 2x+2/((x-1)^2)

What is the first derivative of x^2-1-((x+1/(x-1))) ?

The first derivative of x^2-1-((x+1/(x-1))) is 2x+2/((x-1)^2)

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

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

Solution steps

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

Apply the Sum/Difference Rule:

(f \pm g)^{'} = f^{'} \pm g^{'}

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

\frac{d}{d x} (x^{2}) = 2 x

\frac{d}{d x} (1) = 0

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

= 2 x - 0 - (- \frac{2}{( x - 1 ) ^{2}})

Simplify

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

(5 y^{2} - x y) d x + x^{2} d y = 0

\int - \frac{x}{3} d x

\frac{d}{d x} (- sin (2 x) 2)

(x - 1) y^{^{'}} + (x - 2) y = 0

\frac{d}{d x} (- 2 cos (x))

What is the derivative of x^2-1-((x+1/(x-1))) ?
The derivative of x^2-1-((x+1/(x-1))) is 2x+2/((x-1)^2)
What is the first derivative of x^2-1-((x+1/(x-1))) ?
The first derivative of x^2-1-((x+1/(x-1))) is 2x+2/((x-1)^2)