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

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

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

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

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

- \frac{1}{x ^{3}}

Solution steps

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

Apply the Quotient Rule:

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

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

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

\frac{d}{d x} (x^{2} ln (x^{2})) = 4 x ln (x) + 2 x

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

Simplify

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

= - \frac{1}{x ^{3}}

3 \frac{d y}{d x} + 12 y = 4

\frac{\partial}{\partial y} (4 x sin (x y))

\frac{d x}{d t} = 1.2 x (1 - \frac{x}{4200})

\frac{\partial}{\partial x} (\frac{( 2 π \cdot l )}{x})

\int x^{3} + 2 x^{2} - 1 d x

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