Verified answer

f(x)=4∛x-3/(4x^6 ); taking it as f(x)=(4∛x)-{3/(4x^6 )}, we have

f'(x) = (4/3)∛(1/x^2) + (3/4)*(6)(1/x^7) or

= [{(4/3)∛(1/x^2)}*{1/(8x^7)}]

f(x) = 4x^(1/3) - 3(4x^6)^-1

f '(x) = 4x^(-2/3)/3 + 3(4x^6)^-2 * 24x^5

f '(x) = 4/(3x^(2/3)) + 72x^5/(4x^6)^2

f '(x) = 4/(3x^(2/3)) + 9/(2x^7)