What is the derivative of ln(3x) ?

The derivative of ln(3x) is 1/x

What is the first derivative of ln(3x) ?

The first derivative of ln(3x) is 1/x

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derivative of

ln (3 x)

\frac{1}{x}

Solution steps

\frac{d}{d x} (ln (3 x))

Apply the chain rule:

\frac{1}{3 x} \frac{d}{d x} (3 x)

= \frac{1}{3 x} \frac{d}{d x} (3 x)

\frac{d}{d x} (3 x) = 3

= \frac{1}{3 x} \cdot 3

Simplify

\frac{1}{3 x} \cdot 3 : \frac{1}{x}

= \frac{1}{x}

(x^{3} - 4 x)^{10}

\int \frac{1}{x ^{2} + 7 x + 12} d x

\int (sec (x) tan (x) - (sec (x))^{2}) d x

\frac{d}{d x} (\frac{[ 3 x ^{2} ]}{[ x ^{2} - 4 ]})

f (x) = 3 x^{\frac{1}{3}} - 5 x^{\frac{4}{3}}