Can someone please help me to verify whether the derivative of the following function:
$$z(\zeta)=\frac{R}{2}\left[a\left(\frac{1}{\zeta}+\sum_{k=1}^{N}m_k\zeta^k\right)+b\left(\zeta+\sum_{k=1}^{N}\frac{m_k}{\zeta^k}\right)\right]$$
with respect to $\zeta$
is this one below? $$\frac{dz}{d\zeta}=\frac{R}{2}\left[a\left(-\frac{1}{\zeta^2}+\sum_{k=1}^{N}km_k\zeta^{k-1}\right)+b\left(1-\sum_{k=1}^{N}km_k\zeta^{-k-1}\right)\right]$$
in which $m_k$, $R$, $a$ and $b$ are all constants.
Can someone please help me to verify? I am just not so sure about my own result.
The above derivation is correct.
$$\frac{dz}{d\zeta}=\frac{R}{2}\left[a\left(-\frac{1}{\zeta^2}+\sum_{k=1}^{N}km_k\zeta^{k-1}\right)+b\left(1-\sum_{k=1}^{N}km_k\zeta^{-k-1}\right)\right]$$