What is the derivative of (ln(x))^5 ?

The derivative of (ln(x))^5 is (5ln^4(x))/x

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

The first derivative of (ln(x))^5 is (5ln^4(x))/x

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derivative of

(ln (x))^{5}

\frac{5 ln ^{4} ( x )}{x}

Solution steps

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

Apply the chain rule:

5 (ln (x))^{4} \frac{d}{d x} (ln (x))

= 5 (ln (x))^{4} \frac{d}{d x} (ln (x))

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

= 5 (ln (x))^{4} \frac{1}{x}

Simplify

5 ln^{4} (x) \frac{1}{x} : \frac{5 ln ^{4} ( x )}{x}

= \frac{5 ln ^{4} ( x )}{x}

\int \frac{x - 2 x ^{2} + 1}{x} d x

r \to \infty lim (ln (r))

\int \frac{( x - 1 )}{( x ^{3} - x ^{2} - 2 x )} d x

f (x) = (x^{3} - 7^{x} + 3), at x = 1

y^{^{''}} - 9 y^{^{'}} = 7 t

What is the derivative of (ln(x))^5 ?
The derivative of (ln(x))^5 is (5ln^4(x))/x
What is the first derivative of (ln(x))^5 ?
The first derivative of (ln(x))^5 is (5ln^4(x))/x