Final answer:
To find the derivative, f'(a), of the function f(x) = 1/sqrt(x⁶), we can use the power rule for differentiation.
Step-by-step explanation:
To find the derivative, f'(a), of the function f(x) = 1/sqrt(x⁶), we can use the power rule for differentiation.
First, rewrite the function as f(x) = x^(-3/2). Then, apply the power rule by multiplying the exponent by the coefficient, resulting in the derivative f'(x) = (-3/2)x^(-3/2 - 1).
Finally, substitute the value a into the derivative to get f'(a) = (-3/2)a^(-3/2 - 1).