What is the derivative of ln(x^{16}) ?

The derivative of ln(x^{16}) is (16)/x

What is the first derivative of ln(x^{16}) ?

The first derivative of ln(x^{16}) is (16)/x

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\frac{d}{d x} (ln (x^{16}))

\frac{16}{x}

Solution steps

\frac{d}{d x} (ln (x^{16}))

Apply the chain rule:

\frac{1}{x ^{16}} \frac{d}{d x} (x^{16})

= \frac{1}{x ^{16}} \frac{d}{d x} (x^{16})

\frac{d}{d x} (x^{16}) = 16 x^{15}

= \frac{1}{x ^{16}} \cdot 16 x^{15}

Simplify

\frac{1}{x ^{16}} \cdot 16 x^{15} : \frac{16}{x}

= \frac{16}{x}

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What is the derivative of ln(x^{16}) ?
The derivative of ln(x^{16}) is (16)/x
What is the first derivative of ln(x^{16}) ?
The first derivative of ln(x^{16}) is (16)/x