Originally Posted by

**Soroban** Hello, sara213!

Are you *sure* you know your differentiation rules?

You can use the Quotient Rule,

. . which ends with "over the denominator squared".

Or use an easier way . . .

We have: .$\displaystyle f(x) \:=\:6000\left[1 + 49(0.6^x)\right]^{-1}$

Chain Rule: .$\displaystyle f'(x) \;=\;6000\cdot(\text{-}1)\left[1 + 49(0.6^x)\right]^{-2} \cdot \frac{d}{dx}\left[1 + 49(0.6^x)\right] $

. . . . . . . . . .$\displaystyle f'(x) \;=\;\frac{-6000}{[1 + 49(0.6^x)]^2} \cdot \frac{d}{dx}\left[1 + 49(0.6^x)\right]$