What is the derivative of (ln(x)^6) ?

The derivative of (ln(x)^6) is (6ln^5(x))/x

What is the first derivative of (ln(x)^6) ?

The first derivative of (ln(x)^6) is (6ln^5(x))/x

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\frac{d}{d x} ((ln (x))^{6})

\frac{6 ln ^{5} ( x )}{x}

Solution steps

\frac{d}{d x} ((ln (x))^{6})

Apply the chain rule:

6 (ln (x))^{5} \frac{d}{d x} (ln (x))

= 6 (ln (x))^{5} \frac{d}{d x} (ln (x))

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

= 6 (ln (x))^{5} \frac{1}{x}

Simplify

6 ln^{5} (x) \frac{1}{x} : \frac{6 ln ^{5} ( x )}{x}

= \frac{6 ln ^{5} ( x )}{x}

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

\frac{1}{1 - x}, 24

\int 8 x + 2 d x

\int ln (x) x d x

(\frac{1}{x ^{2}} - \frac{5}{x ^{4}}) (x + 7 x^{3})

What is the derivative of (ln(x)^6) ?
The derivative of (ln(x)^6) is (6ln^5(x))/x
What is the first derivative of (ln(x)^6) ?
The first derivative of (ln(x)^6) is (6ln^5(x))/x