What is the derivative of y = 283.4 * 0.973 ^ x ?

Question

Sorry about the odd numbers, it's the equation for a regression line and my calculus is pretty rusty. Thanks in advance.

Answer 1

y = 283.4 * 0.973 ^ x
lny = ln(283.4) + xln(0.973)
dy/y = ln(0.973)dx
dy/dx = ln(0.973)y
dy/dx = ln(0.973)283.4 * 0.973 ^ x

Answer 2

283.4*0.973=275.748 has the same format of e (decimal places are different).

e = 2.72

If that is the case:

(d/dx) (e^x) = e^x

Since the natural logarithm of e is 1, the derivative of e^(x) is e^(x).

Answer 3

derivative=283.4*0.973=275.7482