What is the derivative of ln(ax^n) ?

The derivative of ln(ax^n) is n/x

What is the first derivative of ln(ax^n) ?

The first derivative of ln(ax^n) is n/x

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\frac{d}{d x} (ln (a x^{n}))

\frac{n}{x}

Solution steps

\frac{d}{d x} (ln (a x^{n}))

Apply the chain rule:

\frac{1}{a x ^{n}} \frac{d}{d x} (a x^{n})

= \frac{1}{a x ^{n}} \frac{d}{d x} (a x^{n})

\frac{d}{d x} (a x^{n}) = an x^{n - 1}

= \frac{1}{a x ^{n}} an x^{n - 1}

Simplify

\frac{1}{a x ^{n}} an x^{n - 1} : \frac{n}{x}

= \frac{n}{x}

x \to \infty lim (5^{- x})

\frac{2 t}{4 + t ^{2}}

x \to 0 lim (\frac{5 x ^{3}}{x ^{3}})

x y^{2} d y = (x^{3} + y^{3}) d x

\frac{d}{d x} ((2 x^{2} - 1)^{3})

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