What is the derivative of y=(ln(x))^3 ?

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

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

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

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derivative of

y = (ln (x))^{3}

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

Solution steps

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

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}

d er i v a t i v e f (x) = e^{2 - x}

t an g e n t x^{2} + 3, at (x = 1)

in v erse l a pl a ce \frac{s ^{2} - 1}{s ^{4} + 3 s ^{2} + 2}

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

d er i v a t i v e - t

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