Question

Find the 5th derivative by using calculus with full workings of 7g^8+2g^7+4g^6+3g^5+g^2+5g+276.3

Answer 1

This is an exercise in applying the power rule, which says

$f(x) = x^n \implies f'(x) = nx^{n-1}$

Starting with

$7g^8 + 2g^7 + 4g^6 + 3g^5 + g^2 + 5g + 276.3$

we have

• first derivative

$56g^7 + 14g^6 + 24g^5 + 15g^4 + 2g + 5$

• second derivative

$392g^6 + 84g^5 + 120g^4 + 60g^3 + 2$

• third derivative

$2352g^5 + 420g^4 + 480g^3 + 180g^2$

• fourth derivative

$11760g^4 + 1680g^3 + 1440g^2 + 360g$

• fifth derivative

$\boxed{47040g^3 + 5040g^2 + 2880g + 360}$