What is the derivative of y=(ln(x))^4 ?

The derivative of y=(ln(x))^4 is (4ln^3(x))/x

What is the first derivative of y=(ln(x))^4 ?

The first derivative of y=(ln(x))^4 is (4ln^3(x))/x

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derivative of

y = (ln (x))^{4}

\frac{4 ln ^{3} ( x )}{x}

Solution steps

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

Apply the chain rule:

4 (ln (x))^{3} \frac{d}{d x} (ln (x))

= 4 (ln (x))^{3} \frac{d}{d x} (ln (x))

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

= 4 (ln (x))^{3} \frac{1}{x}

Simplify

4 ln^{3} (x) \frac{1}{x} : \frac{4 ln ^{3} ( x )}{x}

= \frac{4 ln ^{3} ( x )}{x}

What is the derivative of y=(ln(x))^4 ?
The derivative of y=(ln(x))^4 is (4ln^3(x))/x
What is the first derivative of y=(ln(x))^4 ?
The first derivative of y=(ln(x))^4 is (4ln^3(x))/x