(Solved): Calculate \( y^{(k)}(0) \) for \( 0 \leq k \leq 5 \), where \( y=8 x^{4}+a x^{3}+b x^{2}+c x+d \) ...

Calculate \( y^{(k)}(0) \) for \( 0 \leq k \leq 5 \), where \( y=8 x^{4}+a x^{3}+b x^{2}+c x+d \) (with a,b,c, \( \mathrm{d} \) the constants) \[ \begin{array}{l} y^{(0)}(0)= \\ y^{(1)}(0)= \\ y^{(2)}(0)= \\ y^{(3)}(0)= \\ y^{(4)}(0)= \\ y^{(5)}(0)= \end{array} \]