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Popular >

d/(dz)((z+i)/(z-i))

Solution

\frac{d}{d z} (\frac{z + i}{z - i})

Solution

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

Solution steps

\frac{d}{d z} (\frac{z + i}{z - i})

Apply the Quotient Rule:

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

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

\frac{d}{d z} (z + i) = 1

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

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

Simplify

\frac{1 \cdot ( z - i ) - 1 \cdot ( z + i )}{( z - i ) ^{2}} : - \frac{2 i}{( z - i ) ^{2}}

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

Graph

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Frequently Asked Questions (FAQ)

What is the d/(dz)((z+i)/(z-i)) ?
The d/(dz)((z+i)/(z-i)) is -(2i)/((z-i)^2)
What is the first d/(dz)((z+i)/(z-i)) ?
The first d/(dz)((z+i)/(z-i)) is -(2i)/((z-i)^2)