Final answer:
To find g'(a) for the function g(x)=x^(2/3), use the power rule of differentiation to get g'(x) = (2/3)*x^(-1/3) and then substitute 'a' for 'x' to obtain g'(a) = (2/3)*(1/√³a).
Step-by-step explanation:
The question involves finding the derivative of the function g(x)=x^(2/3) evaluated at a given point 'a' where 'a' is not equal to 0.
To do this, we can apply the power rule of differentiation, which states that if g(x) = x^n, then g'(x) = n*x^(n-1). Applying this rule to our function, we obtain the derivative g'(x) = (2/3)*x^(-1/3).
To find g'(a), we simply substitute 'x' with 'a': g'(a) = (2/3)*a^(-1/3), which can also be written as g'(a) = (2/3)*(1/√³a).