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

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

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

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

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

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

Solution steps

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

Apply the Quotient Rule:

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

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

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

\frac{d x}{d x} = 1

= \frac{\frac{2 l n ( x )}{x} x - 1 \cdot ( ln ( x ) ) ^{2}}{x ^{2}}

Simplify

\frac{\frac{2 l n ( x )}{x} x - 1 \cdot ln ^{2} ( x )}{x ^{2}} : \frac{2 ln ( x ) - ln ^{2} ( x )}{x ^{2}}

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

x y^{^{'}} + 2 y = 6 x^{2} y

\int \frac{x ^{'}}{x} d x

x \to - \infty lim (- 4)

\int e^{u} d u

\frac{100}{s ^{3} ( s - 2 )}

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