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

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

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

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

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derivative of

ln (x^{8})

\frac{8}{x}

Solution steps

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

Apply the chain rule:

\frac{1}{x ^{8}} \frac{d}{d x} (x^{8})

= \frac{1}{x ^{8}} \frac{d}{d x} (x^{8})

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

= \frac{1}{x ^{8}} \cdot 8 x^{7}

Simplify

\frac{1}{x ^{8}} \cdot 8 x^{7} : \frac{8}{x}

= \frac{8}{x}

\frac{d}{d x} ((\frac{x ^{2} + 4}{x ^{2} - 4})^{5})

\frac{d ^{3}}{d x ^{3}} ((2 x + 5)^{7})

\frac{d}{d x} (x^{s i n^{2} (x)})

\frac{d}{d a} (\frac{π ( 9 a ^{2} - 1 )}{54 a ^{2}})

\frac{\partial}{\partial x} (5)

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