What is the derivative of (ln(x)^9) ?

The derivative of (ln(x)^9) is (9ln^8(x))/x

What is the first derivative of (ln(x)^9) ?

The first derivative of (ln(x)^9) is (9ln^8(x))/x

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\frac{d}{d x} ((ln (x))^{9})

\frac{9 ln ^{8} ( x )}{x}

Solution steps

\frac{d}{d x} ((ln (x))^{9})

Apply the chain rule:

9 (ln (x))^{8} \frac{d}{d x} (ln (x))

= 9 (ln (x))^{8} \frac{d}{d x} (ln (x))

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

= 9 (ln (x))^{8} \frac{1}{x}

Simplify

9 ln^{8} (x) \frac{1}{x} : \frac{9 ln ^{8} ( x )}{x}

= \frac{9 ln ^{8} ( x )}{x}

\int 9 e^{x} d x

\int \frac{9 x ^{2} + x + 9}{( x ^{2} + 1 ) ^{2}} d x

f (x) = \frac{x + 2}{x - 1}

\int cot^{5} (θ) sin^{4} (θ) d θ

x \to 0 lim (x^{6} cos (\frac{7}{x}))

What is the derivative of (ln(x)^9) ?
The derivative of (ln(x)^9) is (9ln^8(x))/x
What is the first derivative of (ln(x)^9) ?
The first derivative of (ln(x)^9) is (9ln^8(x))/x