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

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

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

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

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\frac{d}{d x} ((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}

\frac{\partial}{\partial x} (\frac{1}{x - b})

d er i v a t i v e f (x) = \frac{( 10 - 3 x ) + 2}{2}

\int \frac{x ^{2}}{x ^{3} + 3} d x

\frac{\partial}{\partial x} (x^{2} \cdot sin^{2} (yz))

a re a y = x, y = x + 6, 0 < x < 5

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