Question

How do you differentiate `f(x)=(x-1)(1/(x+3)^3)` using the product rule?

Answer 1

`f'(x) = frac{2(3-x)}{(x+3)^{4}}`

Explanation:

`f(x) = (x-1) (x+3)^{-3}`

`f'(x) = frac{d}{dx}( (x-1) (x+3)^{-3} )`

`= (x+3)^{-3} frac{d}{dx}( x-1 ) + (x-1) frac{d}{dx}( (x+3)^{-3} )`

`= (x+3)^{-3} ( 1 ) + (x-1) ( (-3) (x+3)^{-4} (1) )`

`= (x+3)^{-4} ( (x+3) - 3 (x-1) )`

`= frac{2(3-x)}{(x+3)^{4}}`