Question

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

Answer 1

`3/x`

Explanation:

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`