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

The derivative of (ln(x)^{13}) is (13ln^{12}(x))/x

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

The first derivative of (ln(x)^{13}) is (13ln^{12}(x))/x

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

\frac{13 ln ^{12} ( x )}{x}

Solution steps

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

Apply the chain rule:

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

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

\frac{d}{d x} (ln (x)) = \frac{1}{x}

= 13 (ln (x))^{12} \frac{1}{x}

Simplify

13 ln^{12} (x) \frac{1}{x} : \frac{13 ln ^{12} ( x )}{x}

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

(8 x^{2} + 9) (x^{2} - \frac{1}{x})

6 x^{2} - 4 x + 5

\int \frac{( x ^{4} - 5 x ^{2} + 3 x - 4 )}{x} d x

\int_{1}^{e} (\frac{x ^{2} - 1}{x}) d x

\frac{d}{d x} (ln (\frac{x + y}{x - y}))

What is the derivative of (ln(x)^{13}) ?
The derivative of (ln(x)^{13}) is (13ln^{12}(x))/x
What is the first derivative of (ln(x)^{13}) ?
The first derivative of (ln(x)^{13}) is (13ln^{12}(x))/x