What is the d/(dz)((ze^{iz})/((z-2)(z+1))) ?

The d/(dz)((ze^{iz})/((z-2)(z+1))) is

What is the first d/(dz)((ze^{iz})/((z-2)(z+1))) ?

The first d/(dz)((ze^{iz})/((z-2)(z+1))) is

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

\frac{d}{d z} (\frac{z e ^{i z}}{( z - 2 ) ( z + 1 )})

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

Solution steps

\frac{d}{d z} (\frac{z e ^{i z}}{( z - 2 ) ( z + 1 )})

Simplify

\frac{z e ^{i z}}{( z - 2 ) ( z + 1 )} : \frac{z cos ( z )}{- 2 - z + z ^{2}} + i \frac{z sin ( z )}{- 2 - z + z ^{2}}

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

Apply the Sum/Difference Rule:

(f \pm g)^{'} = f^{'} \pm g^{'}

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

\frac{d}{d z} (\frac{z cos ( z )}{- 2 - z + z ^{2}}) = \frac{- z ^{3} sin ( z ) - z ^{2} cos ( z ) + z ^{2} sin ( z ) + 2 z sin ( z ) - 2 cos ( z )}{( - 2 - z + z ^{2} ) ^{2}}

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

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

Simplify

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

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

\int (2 x - 2) e^{- x} d x

\frac{d}{d x} (5 x^{7} e^{x})

y^{^{'}} = 5 x + y, y (0) = 6

\int l x d x

x^{l n (3)}

What is the d/(dz)((ze^{iz})/((z-2)(z+1))) ?
The d/(dz)((ze^{iz})/((z-2)(z+1))) is
What is the first d/(dz)((ze^{iz})/((z-2)(z+1))) ?
The first d/(dz)((ze^{iz})/((z-2)(z+1))) is