What is the derivative of 4/((x-1)) ?

The derivative of 4/((x-1)) is -4/((x-1)^2)

What is the first derivative of 4/((x-1)) ?

The first derivative of 4/((x-1)) is -4/((x-1)^2)

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derivative

- \frac{4}{( x - 1 ) ^{2}}

Solution steps

\frac{d}{d x} (\frac{4}{x - 1})

Take the constant out:

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

= 4 \frac{d}{d x} (\frac{1}{x - 1})

Apply exponent rule:

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

= 4 \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

= 4 (- \frac{1}{( x - 1 ) ^{2}} \cdot 1)

Simplify

4 (- \frac{1}{( x - 1 ) ^{2}} \cdot 1) : - \frac{4}{( x - 1 ) ^{2}}

= - \frac{4}{( x - 1 ) ^{2}}

What is the derivative of 4/((x-1)) ?
The derivative of 4/((x-1)) is -4/((x-1)^2)
What is the first derivative of 4/((x-1)) ?
The first derivative of 4/((x-1)) is -4/((x-1)^2)