How do you use the chain rule to differentiate 1/ln(4x)?

1 Answer
Mar 28, 2017

Let u = 4x, v = ln(u) = ln(4x).

Differentiating the above equation yields

frac{du}{dx} = 4
frac{dv}{du} = 1/u

Then,

1/ln(4x) = 1/v

frac{d}{dx}(1/ln(4x)) = frac{d}{dx}(1/v)

= frac{d}{dv}(1/v) frac{dv}{du} frac{du}{dx}

= (-1/v^2) * (1/u) * (4)

= (-1/(ln(4x))^2) * (1/{4x}) * (4)

= -1/(x (ln(4x))^2 )