What is the derivative of (ln(x^3)/(ln(x^2))) ?

The derivative of (ln(x^3)/(ln(x^2))) is 0

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

The first derivative of (ln(x^3)/(ln(x^2))) is 0

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\frac{d}{d x} (\frac{ln ( x ^{3} )}{ln ( x ^{2} )})

0

Solution steps

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

\frac{d}{d x} (ln (x^{3})) = \frac{3}{x}

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

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

Simplify

\frac{\frac{3}{x} ln ( x ^{2} ) - \frac{2}{x} ln ( x ^{3} )}{ln ^{2} ( x ^{2} )} : 0

= 0

What is the derivative of (ln(x^3)/(ln(x^2))) ?
The derivative of (ln(x^3)/(ln(x^2))) is 0
What is the first derivative of (ln(x^3)/(ln(x^2))) ?
The first derivative of (ln(x^3)/(ln(x^2))) is 0