What is the derivative of (ln(x)^8) ?

The derivative of (ln(x)^8) is (8ln^7(x))/x

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

The first derivative of (ln(x)^8) is (8ln^7(x))/x

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

\frac{8 ln ^{7} ( x )}{x}

Solution steps

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

Apply the chain rule:

8 (ln (x))^{7} \frac{d}{d x} (ln (x))

= 8 (ln (x))^{7} \frac{d}{d x} (ln (x))

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

= 8 (ln (x))^{7} \frac{1}{x}

Simplify

8 ln^{7} (x) \frac{1}{x} : \frac{8 ln ^{7} ( x )}{x}

= \frac{8 ln ^{7} ( x )}{x}

y^{^{''}} + 4 y^{^{'}} + 4 y = \frac{( e ^{2 x} )}{( x )}

\frac{A}{y ^{8}} + B e^{y}

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10 sin (80 π t)

What is the derivative of (ln(x)^8) ?
The derivative of (ln(x)^8) is (8ln^7(x))/x
What is the first derivative of (ln(x)^8) ?
The first derivative of (ln(x)^8) is (8ln^7(x))/x