What is the derivative of ln(x^{11}) ?

The derivative of ln(x^{11}) is (11)/x

What is the first derivative of ln(x^{11}) ?

The first derivative of ln(x^{11}) is (11)/x

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\frac{d}{d x} (ln (x^{11}))

\frac{11}{x}

Solution steps

\frac{d}{d x} (ln (x^{11}))

Apply the chain rule:

\frac{1}{x ^{11}} \frac{d}{d x} (x^{11})

= \frac{1}{x ^{11}} \frac{d}{d x} (x^{11})

\frac{d}{d x} (x^{11}) = 11 x^{10}

= \frac{1}{x ^{11}} \cdot 11 x^{10}

Simplify

\frac{1}{x ^{11}} \cdot 11 x^{10} : \frac{11}{x}

= \frac{11}{x}

What is the derivative of ln(x^{11}) ?
The derivative of ln(x^{11}) is (11)/x
What is the first derivative of ln(x^{11}) ?
The first derivative of ln(x^{11}) is (11)/x