Answer:
14%
Step-by-step explanation:
A = P(1 +rt) . . . . . . . . . . . . . . . . . . formula for the balance for simple interest
2848.52 = 2006(1 +3r) . . . . . . . filling in the given numbers
1.42 = 1 +3r . . . . . . . . . . . . . . . . . .divide by 2006
0.42 = 3r . . . . . . . . . . subtract 1
0.14 = r = 14%
Nancy's account paid interest at 14% per year.
Answer:
h'(x) = (-x² ln x + x² + 1) / (x (x² + 1)^(³/₂))
Step-by-step explanation:
h(x) = ln x / √(x² + 1)
You can either use quotient rule, or you can rewrite using negative exponents and use product rule.
h(x) = (ln x) (x² + 1)^(-½)
h'(x) = (ln x) (-½) (x² + 1)^(-³/₂) (2x) + (1/x) (x² + 1)^(-½)
h'(x) = (-x ln x) (x² + 1)^(-³/₂) + (1/x) (x² + 1)^(-½)
h'(x) = (x² + 1)^(-³/₂) (-x ln x + (1/x) (x² + 1))
h'(x) = (1/x) (x² + 1)^(-³/₂) (-x² ln x + x² + 1)
h'(x) = (-x² ln x + x² + 1) / (x (x² + 1)^(³/₂))
