What is the derivative of (x-0.5/((x+0.5+i)^2)) ?

The derivative of (x-0.5/((x+0.5+i)^2)) is (-x^2+x+2i-0.25)/((x+0.5+i)^4)

What is the first derivative of (x-0.5/((x+0.5+i)^2)) ?

The first derivative of (x-0.5/((x+0.5+i)^2)) is (-x^2+x+2i-0.25)/((x+0.5+i)^4)

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\frac{d}{d x} (\frac{x - 0.5}{( x + 0.5 + i ) ^{2}})

\frac{- x ^{2} + x + 2 i - 0.25}{( x + 0.5 + i ) ^{4}}

Solution steps

\frac{d}{d x} (\frac{x - 0.5}{( x + 0.5 + i ) ^{2}})

Apply the Quotient Rule:

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

= \frac{\frac{d}{d x} ( x - 0.5 ) ( x + 0.5 + i ) ^{2} - \frac{d}{d x} ( ( x + 0.5 + i ) ^{2} ) ( x - 0.5 )}{( ( x + 0.5 + i ) ^{2} ) ^{2}}

\frac{d}{d x} (x - 0.5) = 1

\frac{d}{d x} ((x + 0.5 + i)^{2}) = (2 x + 1) + 2 i

= \frac{1 \cdot ( x + 0.5 + i ) ^{2} - ( 2 x + 1 + 2 i ) ( x - 0.5 )}{( ( x + 0.5 + i ) ^{2} ) ^{2}}

Simplify

\frac{1 \cdot ( x + 0.5 + i ) ^{2} - ( 2 x + 1 + 2 i ) ( x - 0.5 )}{( ( x + 0.5 + i ) ^{2} ) ^{2}} : \frac{- x ^{2} + x + 2 i - 0.25}{( x + 0.5 + i ) ^{4}}

= \frac{- x ^{2} + x + 2 i - 0.25}{( x + 0.5 + i ) ^{4}}

y = x^{4} + 3 e^{x}, (0, 3)

\int x (sin (x) - 2) d x

\frac{\partial}{\partial x} (4^{(x^{9})})

\frac{d ^{2}}{d x ^{2}} (4 cos (x))

What is the derivative of (x-0.5/((x+0.5+i)^2)) ?
The derivative of (x-0.5/((x+0.5+i)^2)) is (-x^2+x+2i-0.25)/((x+0.5+i)^4)
What is the first derivative of (x-0.5/((x+0.5+i)^2)) ?
The first derivative of (x-0.5/((x+0.5+i)^2)) is (-x^2+x+2i-0.25)/((x+0.5+i)^4)