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

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

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

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

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derivative of

ln^{3} (x)

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

Solution steps

\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}

\frac{d y}{d x} = \frac{( 1 - 3 y ) ^{2}}{x}, y (1) = 1

\frac{d}{d x} ((x^{2} + 1)^{2})

n = 0 \sum \infty \frac{n ^{2}}{n !}

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

\frac{\partial}{\partial y} (ln (x^{2} + y^{2} + 2))

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