Question

What is the first derivative of A(t)= 2000(1.00375)^12t??

Answer 1

d/dt(2000 1.00375^(12 t))
| Factor out constants:
= | 2000 (d/dt(1.00375^(12 t)))
| Use the chain rule, d/dt(1.00375^(12 t)) = ( d1.00375^u)/( du) ( du)/( dt), where u = 12 t and ( d1.00375^u)/( du) = 0.00374299 1.00375^u:
= | 2000 (0.00374299 1.00375^(12 t) (d/dt(12 t)))
| Factor out constants:
= | 7.48597 1.00375^(12 t) (12 (d/dt(t)))
| The derivative of t is 1:
= | 89.8317 1 1.00375^(12 t)