What is the derivative of (ln(6x)/(6x)) ?

The derivative of (ln(6x)/(6x)) is (1-ln(6x))/(6x^2)

What is the first derivative of (ln(6x)/(6x)) ?

The first derivative of (ln(6x)/(6x)) is (1-ln(6x))/(6x^2)

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\frac{d}{d x} (\frac{ln ( 6 x )}{6 x})

\frac{1 - ln ( 6 x )}{6 x ^{2}}

Solution steps

\frac{d}{d x} (\frac{ln ( 6 x )}{6 x})

Take the constant out:

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

= \frac{1}{6} \frac{d}{d x} (\frac{ln ( 6 x )}{x})

Apply the Quotient Rule:

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

= \frac{1}{6} \cdot \frac{\frac{d}{d x} ( ln ( 6 x ) ) x - \frac{d x}{d x} ln ( 6 x )}{x ^{2}}

\frac{d}{d x} (ln (6 x)) = \frac{1}{x}

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

= \frac{1}{6} \cdot \frac{\frac{1}{x} x - 1 \cdot ln ( 6 x )}{x ^{2}}

Simplify

\frac{1}{6} \cdot \frac{\frac{1}{x} x - 1 \cdot ln ( 6 x )}{x ^{2}} : \frac{1 - ln ( 6 x )}{6 x ^{2}}

= \frac{1 - ln ( 6 x )}{6 x ^{2}}

\frac{d y}{d x} = 5 y \cdot e^{x + 6}

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

(x^{2} + 2 x y - 4 y^{2}) d x - (x^{2} - 8 x y - 4 y^{2}) d y = 0

y = \frac{f ( x )}{x ^{9}}

sin (x) cos (x) - sin^{2} (x) + x

What is the derivative of (ln(6x)/(6x)) ?
The derivative of (ln(6x)/(6x)) is (1-ln(6x))/(6x^2)
What is the first derivative of (ln(6x)/(6x)) ?
The first derivative of (ln(6x)/(6x)) is (1-ln(6x))/(6x^2)