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

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

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

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

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derivative of

y = (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_{0}^{1} \int_{2 x}^{2} (x - y) d y d x

\frac{sin ( x )}{4 x}

\int 0.4 x d x

\frac{d}{d x} ((x + (x^{2} - 4)^{3})^{10})

x \to 0 + lim (\frac{x}{- 4 x ^{3} - 8 x})

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