Solved: "Find the indicated derivatives. dzdw if z=1w2−1" - Plainmath

Globokim8

Answered question

2021-10-02

Find the indicated derivatives.

\frac{d z}{d w} if z = \frac{1}{\sqrt{w^{2} - 1}}

Answer & Explanation

Arnold Odonnell

Skilled2021-10-03Added 109 answers

Given,

z = \frac{1}{\sqrt{w^{2} - 1}}

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

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

Step 2
Now differentiating with respect to w, we get

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

= - \frac{1}{2} {(w^{2} - 1)}^{- \frac{1}{2} - 1} \cdot \frac{d (w^{2} - 1)}{d w} [∵ \frac{d (x^{n})}{d x} = n x^{n - 1}]

= - \frac{1}{2} {(w^{2} - 1)}^{- \frac{3}{2}} \cdot (2 w - 0)

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

Jeffrey Jordon

Expert2022-01-31Added 2605 answers

Answer is given below (on video)

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