What is the derivative of (log_{e}(x))/(x^2) ?

The derivative of (log_{e}(x))/(x^2) is (1-2ln(x))/(x^3)

What is the first derivative of (log_{e}(x))/(x^2) ?

The first derivative of (log_{e}(x))/(x^2) is (1-2ln(x))/(x^3)

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derivative of

\frac{lo g _{e} ( x )}{x ^{2}}

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

Solution steps

\frac{d}{d x} (\frac{lo g _{e} ( x )}{x ^{2}})

Apply the Quotient Rule:

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

= \frac{\frac{d}{d x} ( lo g _{e} ( x ) ) x ^{2} - \frac{d}{d x} ( x ^{2} ) lo g _{e} ( x )}{( x ^{2} ) ^{2}}

\frac{d}{d x} (lo g_{e} (x)) = \frac{1}{x}

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

= \frac{\frac{1}{x} x ^{2} - 2 x lo g _{e} ( x )}{( x ^{2} ) ^{2}}

Simplify

\frac{\frac{1}{x} x ^{2} - 2 x lo g _{e} ( x )}{( x ^{2} ) ^{2}} : \frac{1 - 2 ln ( x )}{x ^{3}}

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

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