What is the derivative of (e^{2x})/(ln(6x)) ?

The derivative of (e^{2x})/(ln(6x)) is (2e^{2x}xln(6x)-e^{2x})/(xln^2(6x))

What is the first derivative of (e^{2x})/(ln(6x)) ?

The first derivative of (e^{2x})/(ln(6x)) is (2e^{2x}xln(6x)-e^{2x})/(xln^2(6x))

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derivative of

\frac{e ^{2 x}}{ln ( 6 x )}

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

Solution steps

\frac{d}{d x} (\frac{e ^{2 x}}{ln ( 6 x )})

Apply the Quotient Rule:

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

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

\frac{d}{d x} (e^{2 x}) = e^{2 x} \cdot 2

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

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

Simplify

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

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

n = 3 \sum \infty \frac{1}{n ( n - 1 )}

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

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

\int \frac{1}{x 1 - x} d x

x^{6} (5.1)^{x}

What is the derivative of (e^{2x})/(ln(6x)) ?
The derivative of (e^{2x})/(ln(6x)) is (2e^{2x}xln(6x)-e^{2x})/(xln^2(6x))
What is the first derivative of (e^{2x})/(ln(6x)) ?
The first derivative of (e^{2x})/(ln(6x)) is (2e^{2x}xln(6x)-e^{2x})/(xln^2(6x))