What is the derivative of $ln(x^3)$ ?

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Answer 1 · 2015-12-17T16:02:25

$3/x$

According to the chain rule, $d/dx[ln(u)]=(u')/u$ .

Therefore, $d/dx[ln(x^3)]=(d/dx[x^3])/x^3=(3x^2)/x^3=3/x$

An easier way to do this is to rewrite $ln(x^3)$ first.

$ln(x^3)=3lnx$

$d/dx[3ln(x)]=3d/dx[ln(x)]=3(1/x)=3/x$

What is the derivative of ln(x^3)ln(x^3)?