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

The derivative of ((ln(x)^3)/(x^3)) is (3ln^2(x)(-ln(x)+1))/(x^4)

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

The first derivative of ((ln(x)^3)/(x^3)) is (3ln^2(x)(-ln(x)+1))/(x^4)

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

\frac{3 ln ^{2} ( x ) ( - ln ( x ) + 1 )}{x ^{4}}

Solution steps

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

Apply the Quotient Rule:

(\frac{f}{g})^{'} = \frac{f ^{'} \cdot g - g ^{'} \cdot f}{g ^{2}}

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

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

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

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

Simplify

\frac{\frac{3 l n ^{2} ( x )}{x} x ^{3} - 3 x ^{2} ln ^{3} ( x )}{( x ^{3} ) ^{2}} : \frac{3 ln ^{2} ( x ) ( - ln ( x ) + 1 )}{x ^{4}}

= \frac{3 ln ^{2} ( x ) ( - ln ( x ) + 1 )}{x ^{4}}

x \to 0 lim (x^{2} - 3 x + 1)

\int \frac{ln ∣ x ∣}{x} d x

n = 1 \sum \infty \frac{1}{( 4 n ) ^{2} - 1}

x \to - 1 + lim (- 1)

\frac{d}{d x} (x e^{4 x + 1} + \frac{1}{2})

What is the derivative of ((ln(x)^3)/(x^3)) ?
The derivative of ((ln(x)^3)/(x^3)) is (3ln^2(x)(-ln(x)+1))/(x^4)
What is the first derivative of ((ln(x)^3)/(x^3)) ?
The first derivative of ((ln(x)^3)/(x^3)) is (3ln^2(x)(-ln(x)+1))/(x^4)