Verified answer

f(x) = x^n

f'(x) = n*x^(n - 1)

f(x) = x^4.5 + x*⁵√x + 1/∛x^5

(x^4,5)' = 4.5 * x^3.5

(x*⁵√x)' = (x^6/5)' = 6/5*x^1/5 = 6/5*⁵√x

( 1/∛x^5 )' = (1/x^5/3)' = (x^-5/3)' = -5/3 * x^-8/3 = -5/3 * 1/∛x^8

f'(x) = (x^4.5 + x*⁵√x + 1/∛x^5)' =  4.5 * x^3.5 +  6/5*⁵√x - 5/3 * 1/∛x^8