Question

Hey guys, real fast


how is the derivative of 3xlnx = 3+ln(x^3)

Answer 1

You will need to use product rule.
The product rule is:

`(d)/(dx)[f(x)g(x)] = f'(x)g(x)+f(x)g'(x)`



`(d)/(dx)( 3x \ln x) =( (d)/(dx)(3x) \cdot \ln x )+ (3x \cdot (d)/(dx)(\ln x))\\\\ = 3\ln x + 3x\cdot (1)/(x)\\\\=3 \ln x + 3`

This can also be written as (using the log rules):

`3 \ln x + 3 = \boxed{\ln(x^3) + 3}`