What is the derivative of $ln (2 x^{8})$ $ln (2x^8)$ ?

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Answer 1 · 2017-02-05T16:12:18

$\frac{d}{d x} ln (2 x^{8}) = \frac{8}{x}$ $d/dx ln(2x^8) = 8/x$

Rather than the chain rule you can use the properties of logarithms:

$ln (2 x^{8}) = ln 2 + 8 ln x$ $ln(2x^8) = ln2 +8lnx$

so:

$\frac{d}{d x} ln (2 x^{8}) = \frac{8}{x}$ $d/dx ln(2x^8) = 8/x$

What is the derivative of ln (2x^8)ln(2x8)ln (2x^8)?