d/(dz)((z^2)/((z-2i)^2))

解答

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

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

求解步骤

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

使用微分除法定则:

(\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}}

化简

\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}}

\frac{d}{d x} ((1 + 2 sin (x)) sin (x))

\int \frac{x arctan ( x )}{( 1 + x ^{2} ) ^{2}} d x

\int_{0}^{1} 2 π (x + 8) x^{2} d x

x \to - 2 lim (- 3 x^{2} - 6 x + 4)

d er i v a t i v e sin (5) x^{2}