What is the derivative of (e^{7x})/(ln(6x)) ?

The derivative of (e^{7x})/(ln(6x)) is (7e^{7x}xln(6x)-e^{7x})/(xln^2(6x))

What is the first derivative of (e^{7x})/(ln(6x)) ?

The first derivative of (e^{7x})/(ln(6x)) is (7e^{7x}xln(6x)-e^{7x})/(xln^2(6x))

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derivative of

\frac{e ^{7 x}}{ln ( 6 x )}

\frac{7 e ^{7 x} x ln ( 6 x ) - e ^{7 x}}{x ln ^{2} ( 6 x )}

Solution steps

\frac{d}{d x} (\frac{e ^{7 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 ^{7 x} ) ln ( 6 x ) - \frac{d}{d x} ( ln ( 6 x ) ) e ^{7 x}}{( ln ( 6 x ) ) ^{2}}

\frac{d}{d x} (e^{7 x}) = e^{7 x} \cdot 7

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

= \frac{e ^{7 x} \cdot 7 ln ( 6 x ) - \frac{1}{x} e ^{7 x}}{( ln ( 6 x ) ) ^{2}}

Simplify

\frac{e ^{7 x} \cdot 7 ln ( 6 x ) - \frac{1}{x} e ^{7 x}}{ln ^{2} ( 6 x )} : \frac{7 e ^{7 x} x ln ( 6 x ) - e ^{7 x}}{x ln ^{2} ( 6 x )}

= \frac{7 e ^{7 x} x ln ( 6 x ) - e ^{7 x}}{x ln ^{2} ( 6 x )}

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

\frac{d}{d x} (\frac{1}{6 + x ^{2}})

y = \frac{e ^{x}}{x}

f (x) = x^{4} - 17 x^{2} + 16, at x = 2

- x^{2} + 10, - 10, - 1

What is the derivative of (e^{7x})/(ln(6x)) ?
The derivative of (e^{7x})/(ln(6x)) is (7e^{7x}xln(6x)-e^{7x})/(xln^2(6x))
What is the first derivative of (e^{7x})/(ln(6x)) ?
The first derivative of (e^{7x})/(ln(6x)) is (7e^{7x}xln(6x)-e^{7x})/(xln^2(6x))