What is the derivative of (ln(9x)/(9x)) ?

The derivative of (ln(9x)/(9x)) is (1-ln(9x))/(9x^2)

What is the first derivative of (ln(9x)/(9x)) ?

The first derivative of (ln(9x)/(9x)) is (1-ln(9x))/(9x^2)

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\frac{d}{d x} (\frac{ln ( 9 x )}{9 x})

\frac{1 - ln ( 9 x )}{9 x ^{2}}

Solution steps

\frac{d}{d x} (\frac{ln ( 9 x )}{9 x})

Take the constant out:

(a \cdot f)^{'} = a \cdot f^{'}

= \frac{1}{9} \frac{d}{d x} (\frac{ln ( 9 x )}{x})

Apply the Quotient Rule:

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

= \frac{1}{9} \cdot \frac{\frac{d}{d x} ( ln ( 9 x ) ) x - \frac{d x}{d x} ln ( 9 x )}{x ^{2}}

\frac{d}{d x} (ln (9 x)) = \frac{1}{x}

\frac{d x}{d x} = 1

= \frac{1}{9} \cdot \frac{\frac{1}{x} x - 1 \cdot ln ( 9 x )}{x ^{2}}

Simplify

\frac{1}{9} \cdot \frac{\frac{1}{x} x - 1 \cdot ln ( 9 x )}{x ^{2}} : \frac{1 - ln ( 9 x )}{9 x ^{2}}

= \frac{1 - ln ( 9 x )}{9 x ^{2}}

\frac{d}{d x} (\frac{a}{x} + b x)

(17 - 13) (178)

\frac{\partial}{\partial x} (\frac{x}{cos ( y )})

y^{^{'}} = x^{2} - 6 x + 14

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

What is the derivative of (ln(9x)/(9x)) ?
The derivative of (ln(9x)/(9x)) is (1-ln(9x))/(9x^2)
What is the first derivative of (ln(9x)/(9x)) ?
The first derivative of (ln(9x)/(9x)) is (1-ln(9x))/(9x^2)