Derivative of A=620(1.628)^t

Question

I'm uncertain about how to find the derivative of A=620(1.628)^t.

 

I'm quite certain that it has something to do with making (1.628)^t into (1.628)^t * ln(t) but I'm unsure if I have to do something with the 620 as well, help would be appreciated. 

Answer 1

D_x[a^x] = a^x * ln(a).  We also use D_x[C*f(x)] = C*f'(x), where C is a constant.

 

In your problem, a = 1.628, and C is 620.  Using the above rules, we have

D_t[620*1.628^t] =

620*D_t(1.628^t) =

620*1.628^t * ln 1.628.