What is the derivative of 1/((z-1)) ?

The derivative of 1/((z-1)) is -1/((z-1)^2)

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

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

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derivative of

\frac{1}{( z - 1 )}

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

Solution steps

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

Apply exponent rule:

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

= \frac{d}{d z} ((z - 1)^{- 1})

Apply the chain rule:

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

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

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

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

Simplify

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

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