Question

Calc help! A=12000(1+r/52)^520
a) find the rate of change of A with respect to r
-I found the derivative to be 12000(1+r/52)^519, why isn't that correct?

Answer 1

You're missing a zero:
\[
A = 12000(1+\frac{r}{52})^{520}\\
\frac{dA}{dr} = \bigg(520*12000(1+\frac{r}{52})^{519}\bigg) * \frac{d(1+\frac{r}{52})}{dr} \\
= \bigg(6240000(1+\frac{r}{52})^{519}\bigg) * \frac{1}{52} = 120,000(1+\frac{r}{52})^{519}
\]

Answer 2

because the derivative rule is to multiply the coefficient by the exponent and then subtract one from the e exponent \[\large\rm y= ag^2\] \[y'=2a \cdot g\]
and then of course for your question chain rule would work

Answer 3

thank you!!

Answer 4

No problem :)