What is the d/(dz)(((3z+2i))/((4z-5i))) ?

The d/(dz)(((3z+2i))/((4z-5i))) is -(23i)/((4z-5i)^2)

What is the first d/(dz)(((3z+2i))/((4z-5i))) ?

The first d/(dz)(((3z+2i))/((4z-5i))) is -(23i)/((4z-5i)^2)

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\frac{d}{d z} (\frac{( 3 z + 2 i )}{( 4 z - 5 i )})

- \frac{23 i}{( 4 z - 5 i ) ^{2}}

Solution steps

\frac{d}{d z} (\frac{( 3 z + 2 i )}{( 4 z - 5 i )})

Apply the Quotient Rule:

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

= \frac{\frac{d}{d z} ( 3 z + 2 i ) ( 4 z - 5 i ) - \frac{d}{d z} ( 4 z - 5 i ) ( 3 z + 2 i )}{( 4 z - 5 i ) ^{2}}

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

\frac{d}{d z} (4 z - 5 i) = 4

= \frac{3 ( 4 z - 5 i ) - 4 ( 3 z + 2 i )}{( 4 z - 5 i ) ^{2}}

Simplify

\frac{3 ( 4 z - 5 i ) - 4 ( 3 z + 2 i )}{( 4 z - 5 i ) ^{2}} : - \frac{23 i}{( 4 z - 5 i ) ^{2}}

= - \frac{23 i}{( 4 z - 5 i ) ^{2}}

lo g_{10} ((x + 1)^{x + 1})

x^{2} + 2 x - 18

x (lo g_{10} (∣ x ∣) - 1)

y = \frac{2 sin ( x )}{5}

x^{\frac{- 1}{2}}

What is the d/(dz)(((3z+2i))/((4z-5i))) ?
The d/(dz)(((3z+2i))/((4z-5i))) is -(23i)/((4z-5i)^2)
What is the first d/(dz)(((3z+2i))/((4z-5i))) ?
The first d/(dz)(((3z+2i))/((4z-5i))) is -(23i)/((4z-5i)^2)