What is the derivative of ln^2(x/3) ?

The derivative of ln^2(x/3) is (2ln(x/3))/x

What is the first derivative of ln^2(x/3) ?

The first derivative of ln^2(x/3) is (2ln(x/3))/x

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\frac{d}{d x} (ln^{2} (\frac{x}{3}))

\frac{2 ln ( \frac{x}{3} )}{x}

Solution steps

\frac{d}{d x} (ln^{2} (\frac{x}{3}))

Apply the chain rule:

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

= 2 ln (\frac{x}{3}) \frac{d}{d x} (ln (\frac{x}{3}))

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

= 2 ln (\frac{x}{3}) \frac{1}{x}

Simplify

2 ln (\frac{x}{3}) \frac{1}{x} : \frac{2 ln ( \frac{x}{3} )}{x}

= \frac{2 ln ( \frac{x}{3} )}{x}

\int \frac{1}{3 y} d y

\int (\frac{tan ( x )}{cos ^{2} ( x )}) d x

\int x (2 x + 1) d x

n = 1 \sum \infty \frac{1}{2 n + 4}

\int \frac{1}{sin ( x ) sin ( 2 x )} d x

What is the derivative of ln^2(x/3) ?
The derivative of ln^2(x/3) is (2ln(x/3))/x
What is the first derivative of ln^2(x/3) ?
The first derivative of ln^2(x/3) is (2ln(x/3))/x