What is the derivative of ln(xln(x)ln(x)) ?

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

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

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

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

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

Solution steps

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

Simplify

ln (x) ln (x) ln (x) : ln^{3} (x)

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

Apply the chain rule:

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

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

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

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

Simplify

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

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

x^{\frac{1}{7}}

\frac{d}{d y} ((x + y) e^{y})

\frac{d}{d x} ((4 + 8 x) cos (1 - x))

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

\int \frac{4 x + 1}{2 x ^{2} + x - 3} d x

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