Derivative Substitution - # 3

[Jason]

ex. a

What's the solution?

\(\underline{\dfrac{d}{dx}[(\ln(6x))^{3}]}\)


\(\dfrac{d}{dx}[(\ln(6x))^{3}]\)

\(u = 6x\)

\(\dfrac{dy}{dx} = [\dfrac{du}{dx}][\dfrac{dy}{du}]\)

\(\dfrac{dy}{dx} = [6][3(\dfrac{1}{u})^{2}]\)

\(\dfrac{dy}{dx} = 6(3(\dfrac{1}{6x})^{2})\)

\(\dfrac{dy}{dx} = 18(\dfrac{1}{6x})^{2}\)

\(\dfrac{dy}{dx} = 3(\dfrac{1}{x})^{2}\)