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

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

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

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

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derivative of

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

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

Solution steps

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

Apply exponent rule:

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

= \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

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

Simplify

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

(1, 9), (6, 3)

y = (3 x^{2} + 5 x)^{2}

f (x) = \frac{1}{3} x^{3} + 2 x - 4, at x = 3

r = - 3

(- 6, \frac{3 π}{4})

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