What is the derivative of (ln(1/x)^3) ?

The derivative of (ln(1/x)^3) is -(3ln^2(x))/x

What is the first derivative of (ln(1/x)^3) ?

The first derivative of (ln(1/x)^3) is -(3ln^2(x))/x

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

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

Solution steps

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

Simplify

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

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

Take the constant out:

(a \cdot f)^{'} = a \cdot f^{'}

= - \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}

\int x + 2 π d x

\int (x + 1) e^{x} d x

\frac{\partial}{\partial x} (x^{2} + 8 x y + y^{2})

x^{s i n (x)}

f (x) = x^{3} + x^{2} - x - 1, at x = 0

What is the derivative of (ln(1/x)^3) ?
The derivative of (ln(1/x)^3) is -(3ln^2(x))/x
What is the first derivative of (ln(1/x)^3) ?
The first derivative of (ln(1/x)^3) is -(3ln^2(x))/x