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Popular >

derivative of ln((x^3/(e^{3x)}))

Solution

\frac{d}{d x} (ln (\frac{x ^{3}}{e ^{3 x}}))

Solution

\frac{3}{x} - 3

Solution steps

\frac{d}{d x} (ln (\frac{x ^{3}}{e ^{3 x}}))

Simplify

ln (\frac{x ^{3}}{e ^{3 x}}) : ln (x^{3}) - 3 x

= \frac{d}{d x} (ln (x^{3}) - 3 x)

Apply the Sum/Difference Rule:

(f \pm g)^{'} = f^{'} \pm g^{'}

= \frac{d}{d x} (ln (x^{3})) - \frac{d}{d x} (3 x)

\frac{d}{d x} (ln (x^{3})) = \frac{3}{x}

\frac{d}{d x} (3 x) = 3

= \frac{3}{x} - 3

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Frequently Asked Questions (FAQ)

What is the derivative of ln((x^3/(e^{3x)})) ?
The derivative of ln((x^3/(e^{3x)})) is 3/x-3
What is the first derivative of ln((x^3/(e^{3x)})) ?
The first derivative of ln((x^3/(e^{3x)})) is 3/x-3