Derivative of ln(3x) with Chain Rule | Calculus 1 Exercises

We differentiate ln(3x) using the chain rule. The outside function f(x) is f(x) = lnx, and the inside function g(x) is g(x)=3x. Then, f(g(x)) = ln(3x), so we see we've identified the outside and inside functions correctly. Applying the chain rule, we have the derivative of f(g(x)) is f'(g(x))*g'(x) = 1/x. #calculus1 #apcalculus

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[justabunga]

You could have also done using properties of logarithms first and then differentiate to make it a lot easier. y=ln(3x)=ln(3)+ln(x), so the derivative is y'=1/x.