Question

How do you differentiate `f(x)=1/(16x+3)^2` using the quotient rule?

Answer 1

`frac{d}{dx}(frac{1}{(16x+3)^2}) = frac{-32}{(16x+3)^3}`

Explanation:

`frac{d}{dx}(frac{1}{(16x+3)^2}) = frac{(16x+3)^2*frac{d}{dx}(1)-(1)frac{d]{dx}((16x+3)^2)}{[(16x+3)^2]^2}`

`= frac{(16x+3)^2*(0)-(1)(2(16x+3)(16))}{(16x+3)^4}`

`= frac{-32}{(16x+3)^3}`