What is the derivative of f(x)= 2/(x-1) ?

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

What is the first derivative of f(x)= 2/(x-1) ?

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

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derivative of

f (x) = \frac{2}{x - 1}

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

Solution steps

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

Take the constant out:

(a \cdot f)^{'} = a \cdot f^{'}

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

Apply exponent rule:

\frac{1}{a} = a^{- 1}

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

Apply the chain rule:

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

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

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

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

Simplify

2 (- \frac{1}{( x - 1 ) ^{2}} \cdot 1) : - \frac{2}{( x - 1 ) ^{2}}

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

- \frac{5}{s ( 50 + 20 s )}

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

\int \frac{x}{( x ^{2} + 1 ) ^{\frac{9}{2}}} d x

- 4 (t - 1)

\int_{0}^{2} e^{5 x} d x

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