What is the derivative of y=ln(x^{13}) ?

The derivative of y=ln(x^{13}) is (13)/x

What is the first derivative of y=ln(x^{13}) ?

The first derivative of y=ln(x^{13}) is (13)/x

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derivative of

y = ln (x^{13})

\frac{13}{x}

Solution steps

\frac{d}{d x} (ln (x^{13}))

Apply the chain rule:

\frac{1}{x ^{13}} \frac{d}{d x} (x^{13})

= \frac{1}{x ^{13}} \frac{d}{d x} (x^{13})

\frac{d}{d x} (x^{13}) = 13 x^{12}

= \frac{1}{x ^{13}} \cdot 13 x^{12}

Simplify

\frac{1}{x ^{13}} \cdot 13 x^{12} : \frac{13}{x}

= \frac{13}{x}

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What is the derivative of y=ln(x^{13}) ?
The derivative of y=ln(x^{13}) is (13)/x
What is the first derivative of y=ln(x^{13}) ?
The first derivative of y=ln(x^{13}) is (13)/x