What is the derivative of (ln(x^5)/(ln(x^4))) ?

The derivative of (ln(x^5)/(ln(x^4))) is 0

What is the first derivative of (ln(x^5)/(ln(x^4))) ?

The first derivative of (ln(x^5)/(ln(x^4))) is 0

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\frac{d}{d x} (\frac{ln ( x ^{5} )}{ln ( x ^{4} )})

0

Solution steps

\frac{d}{d x} (\frac{ln ( x ^{5} )}{ln ( x ^{4} )})

Apply the Quotient Rule:

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

= \frac{\frac{d}{d x} ( ln ( x ^{5} ) ) ln ( x ^{4} ) - \frac{d}{d x} ( ln ( x ^{4} ) ) ln ( x ^{5} )}{( ln ( x ^{4} ) ) ^{2}}

\frac{d}{d x} (ln (x^{5})) = \frac{5}{x}

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

= \frac{\frac{5}{x} ln ( x ^{4} ) - \frac{4}{x} ln ( x ^{5} )}{( ln ( x ^{4} ) ) ^{2}}

Simplify

\frac{\frac{5}{x} ln ( x ^{4} ) - \frac{4}{x} ln ( x ^{5} )}{ln ^{2} ( x ^{4} )} : 0

= 0

\int_{- 2}^{2} (8 - 2 y^{2}) d y

x \to 0 lim (x^{2} + x - x)

\int 3 y 7 - 3 y^{2} d y

\int_{0}^{1} (y^{2} + y^{4}) d y

\frac{d}{d x} (x^{2} 3 x + 1)

What is the derivative of (ln(x^5)/(ln(x^4))) ?
The derivative of (ln(x^5)/(ln(x^4))) is 0
What is the first derivative of (ln(x^5)/(ln(x^4))) ?
The first derivative of (ln(x^5)/(ln(x^4))) is 0