What is the derivative of f(x)=ln(4-x^8) ?

The derivative of f(x)=ln(4-x^8) is -(8x^7)/(4-x^8)

What is the first derivative of f(x)=ln(4-x^8) ?

The first derivative of f(x)=ln(4-x^8) is -(8x^7)/(4-x^8)

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derivative of

f (x) = ln (4 - x^{8})

- \frac{8 x ^{7}}{4 - x ^{8}}

Solution steps

\frac{d}{d x} (ln (4 - x^{8}))

Apply the chain rule:

\frac{1}{4 - x ^{8}} \frac{d}{d x} (4 - x^{8})

= \frac{1}{4 - x ^{8}} \frac{d}{d x} (4 - x^{8})

\frac{d}{d x} (4 - x^{8}) = - 8 x^{7}

= \frac{1}{4 - x ^{8}} (- 8 x^{7})

Simplify

\frac{1}{4 - x ^{8}} (- 8 x^{7}) : - \frac{8 x ^{7}}{4 - x ^{8}}

= - \frac{8 x ^{7}}{4 - x ^{8}}

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What is the derivative of f(x)=ln(4-x^8) ?
The derivative of f(x)=ln(4-x^8) is -(8x^7)/(4-x^8)
What is the first derivative of f(x)=ln(4-x^8) ?
The first derivative of f(x)=ln(4-x^8) is -(8x^7)/(4-x^8)