Final answer:
To find the first and second derivative of the function g(r) = r⁵ * r, apply the power rule for derivatives. The first derivative is 6r^5 and the second derivative is 30r^4.
Step-by-step explanation:
To find the first and second derivative of the function g(r) = r⁵ * r, we need to apply the power rule for derivatives. The power rule states that if we have a function of the form f(x) = x^n, then the derivative of f(x) is given by f'(x) = n * x^(n-1). Applying this rule, we can find the derivatives of g(r).
The first derivative of g(r) is given by g'(r) = 5r^4 * r + r^5 * 1 = 5r^5 + r^5 = 6r^5.
The second derivative of g(r) is given by g''(r) = 6 * 5r^4 = 30r^4.