Question

Find the derivative (t)=t^2/3-t^1/3+4

Answer 1

`f(t)=t^(2)/(3)-t^(1)/(3)+4\\\\f'(t)=\left(t^(2)/(3)-t^(1)/(3)+4\right)'=\left(t^(2)/(3)\right)'-\left(t^(1)/(3)\right)'+(4)'\\\\=(2)/(3)t^{(2)/(3)-1}-(1)/(3)t^{(1)/(3)-1}+0=(2)/(3)t^{-(1)/(3)}-(1)/(3)t^{-(2)/(3)}\\\\\boxed{f'(x)=(2)/(3\left(t^(1)/(3)-t^(2)/(3)\right))}\\\\Used:\\\\\ [f(x)+g(x)]'=f'(x)+g'(x)\\\\(c)'=0\\\\\left(x^n\right)'=nx^(n-1)\\\\a^(-n)=(1)/(a^n)`