Get the solution to "Using the definition, calculate the derivatives of the..."

shadsiei

Answered question

2021-06-04

Using the definition, calculate the derivatives of the functions. Then find the values of the derivatives as specified.

k (z) = \frac{1 - z}{2 z} . k^{'} (- 1), k^{'} (1), k^{'} (\sqrt{2})

Tasneem Almond

Skilled2021-06-05Added 91 answers

Step 1

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

Step 2
Using Quotient Rule

(\frac{f}{g}) = \frac{f^{'} g - g^{'} f}{g^{2}}

Step 3
Using quotient rule to find the derivative

k^{'} (z) = \frac{1}{2} [\frac{1 - z}{z}]

k^{'} (z) = \frac{1}{2} [\frac{z {(1 - z)}^{'} - z^{'} (1 - z)}{z^{2}}]

k^{'} (z) = \frac{1}{2} [\frac{- z - (1 - z)}{z^{2}}]

k^{'} (z) = \frac{1}{2} [\frac{- z - 1 + z}{z^{2}}]

k^{'} (z) = [\frac{1}{2 z^{2}}]

Step 4
Put z=1

k^{'} (1) = [\frac{1}{2}]

Put z=-1

k^{'} (- 1) = [\frac{1}{2}]

put

z = \sqrt{2}

k^{'} (\sqrt{2}) = [\frac{1}{4}]

Do you have a similar question?

Recalculate according to your conditions!

Didn't find what you were looking for?