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

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

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

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

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

\frac{n}{x}

Solution steps

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

Apply the chain rule:

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

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

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

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

Simplify

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

= \frac{n}{x}

\int \frac{30 x ^{3} - 60 x ^{2} + 4}{x ^{2} - 2 x} d x

\int \frac{( e ^{x} )}{( 1 + e ^{x} )} d x

n = 1 \sum \infty \frac{1 0 ^{n}}{n !}

\frac{\partial}{\partial x} (6 e^{x^{6} y})

2 y^{^{''}} - 2 y^{^{'}} + 25 y = 0

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