Expert Answer to "Find the first and second derivatives w =..." - Plainmath

Khadija Wells

Answered question

2021-10-05

Find the first and second derivatives w = 3z-2 - 1/z

Answer & Explanation

pivonie8

Skilled2021-10-06Added 91 answers

Step 1
Consider the following equation:

w = 3 z - 2 - \frac{1}{z}

Differentiate w with respect to z:

\frac{d w}{d z} = \frac{d}{d z} (3 z - 2 - \frac{1}{z})

= \frac{d}{d z} 3 z - \frac{d}{d z} 2 - \frac{d}{d z} z^{- 1}

= 3 - 0 + z^{- 2}

= 3 + \frac{1}{z^{2}}

Step 2
Differentiate

\frac{d w}{d z}

with respect to z:

\frac{d^{2} w}{{d z}^{2}} = \frac{d}{d z} (3 + \frac{1}{z^{2}})

= \frac{d}{d z} 3 + \frac{d}{d z} z^{- 2}

= 0 - 2 z^{- 3}

= - \frac{2}{z^{3}}

Jeffrey Jordon

Expert2022-11-14Added 2605 answers

Answer is given below (on video)

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