What is (\partial)/(\partial x)((ln(x))/(x^2)) ?

The answer to (\partial)/(\partial x)((ln(x))/(x^2)) is (1-2ln(x))/(x^3)

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(\partial)/(\partial x)((ln(x))/(x^2))

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

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

Solution steps

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

Apply the Quotient Rule:

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

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

\frac{\partial}{\partial x} (ln (x)) = \frac{1}{x}

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

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

Simplify

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

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

x y^{^{'}} + y = 3 cos (x), y (π) = 0

\frac{\partial}{\partial x} (e^{x} - x (sin (y)))

\frac{6 x ^{2} + 4 x + 2}{x}

\frac{d}{d x} (- x - 1)

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

What is (\partial)/(\partial x)((ln(x))/(x^2)) ?
The answer to (\partial)/(\partial x)((ln(x))/(x^2)) is (1-2ln(x))/(x^3)