d/(dz)((2cos(z))/(z+1))

해법

\frac{d}{d z} (\frac{2 cos ( z )}{z + 1})

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

솔루션 단계

\frac{d}{d z} (\frac{2 cos ( z )}{z + 1})

정수를 빼라:

(a \cdot f)^{'} = a \cdot f^{'}

= 2 \frac{d}{d z} (\frac{cos ( z )}{z + 1})

상수 규칙 적용:

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

= 2 \cdot \frac{\frac{d}{d z} ( cos ( z ) ) ( z + 1 ) - \frac{d}{d z} ( z + 1 ) cos ( z )}{( z + 1 ) ^{2}}

\frac{d}{d z} (cos (z)) = - sin (z)

\frac{d}{d z} (z + 1) = 1

= 2 \cdot \frac{( - sin ( z ) ) ( z + 1 ) - 1 \cdot cos ( z )}{( z + 1 ) ^{2}}

2 \cdot \frac{( - sin ( z ) ) ( z + 1 ) - 1 \cdot cos ( z )}{( z + 1 ) ^{2}}

간소화하다 :

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

= \frac{2 ( - sin ( z ) ( z + 1 ) - cos ( z ) )}{( z + 1 ) ^{2}}