a) Obliczmy

$f{}^{\prime }\left(z\right)=2z+\frac{a}{2}\cdot \left(-2z^{-3}\right)+a\cdot \frac{1}{2\sqrt{z}}=2z-\frac{a}{z^3}+\frac{a}{2\sqrt{z}}$  

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b) Obliczmy

$f{}^{\prime }\left(t\right)=a\cdot 3t^2+\frac{1}{a}+\left(\frac{t^2-1}{t+1}\right){}^{\prime }=3a{t}^2+\frac{1}{a}+\left(t-1\right){}^{\prime }=3a{t}^2+\frac{1}{a}+1$  

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c) Obliczmy

$f{}^{\prime }\left(y\right)=7a\cdot 6y^5-7\cdot 2y=42a{y}^5-14y$  

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(Uwaga: błędy w odpowiedziach.)