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

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

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

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

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\frac{d}{d x} (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}

\frac{d}{d x} (e^{(- 2 x)})

\int 3 y^{2} (e^{y^{3}} - 1) d y

n = 1001 \sum \infty \frac{1}{n}

\int_{0}^{5} x^{3} x^{2} + 25 d x

x y^{^{'}} + (11 + x) y = e^{- x}

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