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Popular >

((ln^2(x))/x)^'

Solution

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

Solution

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

Solution steps

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

Apply the Quotient Rule:

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

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

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

x^{'} = 1

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

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Frequently Asked Questions (FAQ)

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