This is an exercise in applying the power rule, which says
[tex]f(x) = x^n \implies f'(x) = nx^{n-1}[/tex]
Starting with
[tex]7g^8 + 2g^7 + 4g^6 + 3g^5 + g^2 + 5g + 276.3[/tex]
we have
• first derivative
[tex]56g^7 + 14g^6 + 24g^5 + 15g^4 + 2g + 5[/tex]
• second derivative
[tex]392g^6 + 84g^5 + 120g^4 + 60g^3 + 2[/tex]
• third derivative
[tex]2352g^5 + 420g^4 + 480g^3 + 180g^2[/tex]
• fourth derivative
[tex]11760g^4 + 1680g^3 + 1440g^2 + 360g[/tex]
• fifth derivative
[tex]\boxed{47040g^3 + 5040g^2 + 2880g + 360}[/tex]
