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

The d/(dz)((z^2)/((z+2i)^2)) is (4iz)/((z+2i)^3)

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

The first d/(dz)((z^2)/((z+2i)^2)) is (4iz)/((z+2i)^3)

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

\frac{4 i z}{( z + 2 i ) ^{3}}

Solution steps

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

Apply the Quotient Rule:

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

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

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

\frac{d}{d z} ((z + 2 i)^{2}) = 2 z + 4 i

= \frac{2 z ( z + 2 i ) ^{2} - ( 2 z + 4 i ) z ^{2}}{( ( z + 2 i ) ^{2} ) ^{2}}

Simplify

\frac{2 z ( z + 2 i ) ^{2} - ( 2 z + 4 i ) z ^{2}}{( ( z + 2 i ) ^{2} ) ^{2}} : \frac{4 i z}{( z + 2 i ) ^{3}}

= \frac{4 i z}{( z + 2 i ) ^{3}}

\int 3 cos (\frac{1}{2} x) d x

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

n = 1 \sum \infty ln (\frac{n}{3 n + 1})

\int \frac{3}{x ^{- 1} + 3} d x

\int 6 - x^{2} d x

What is the d/(dz)((z^2)/((z+2i)^2)) ?
The d/(dz)((z^2)/((z+2i)^2)) is (4iz)/((z+2i)^3)
What is the first d/(dz)((z^2)/((z+2i)^2)) ?
The first d/(dz)((z^2)/((z+2i)^2)) is (4iz)/((z+2i)^3)