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

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

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

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

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derivative of

ln (x) ln (2 x)

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

Solution steps

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

Apply the Product Rule:

(f \cdot g)^{'} = f^{'} \cdot g + f \cdot g^{'}

f = ln (x), g = ln (2 x)

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

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

\frac{d}{d x} (ln (2 x)) = \frac{1}{x}

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

Simplify

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

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

\frac{d}{d x} (\frac{4}{2 x ^{2} - ( + 4 ) ( - 3 ) - ( - 6 ) ( - 2 )})

\frac{1}{n ( 1 + ln ( x ) ) ^{2}}

\frac{d}{d y} (\frac{y}{2 x + 1})

\frac{1}{n}

(3 x^{2} + 7) (6 x + 3)

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