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}

\int \frac{sin ^{2} ( θ )}{cos ^{4} ( θ )} d θ

\frac{\partial}{\partial x} (- \frac{v ( x , t )}{b ( x , t ) ( x - v ( x , t ) t )})

\frac{d y}{y} = d x

\frac{1}{x}

\frac{1 - x e ^{x}}{x + e ^{x}}

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