What is the derivative of $f(x)=2lnx^3$ ?

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Answer 1 · 2015-05-26T15:10:17

Using the chain rule, we can rename $u=x^3$ , and thus, start working with $f(x)=f(u)=2ln(u)$ .

The chain rule states that

$(dy)/(dx)=(dy)/(du)(du)/(dx)$

So,

$(dy)/(du)=2*1/u=2/u$

$(du)/(dx)=3x^2$

Thus,

$(dy)/(dx)=2/u*3x^2=(6x^2)/u=(6cancel(x^2))/x^cancel(3)=color(green)(6/x)$

Answer 2 · 2015-05-26T18:10:21

Alternative solution:

$f(x) = 2lnx^3=6lnx$

So,

$f'(x) = 6 * 1/x = 6/x$

What is the derivative of f(x)=2lnx^3f(x)=2lnx^3?