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:
$\frac{d}{dx}[f(x)g(x)] = f'(x)g(x)+f(x)g'(x)$


$\frac{d}{dx}( 3x \ln x) =( \frac{d}{dx}(3x) \cdot \ln x )+ (3x \cdot \frac{d}{dx}(\ln x))\\\\ = 3\ln x + 3x\cdot \frac{1}{x}\\\\=3 \ln x + 3$

This can also be written as (using the log rules):
$3 \ln x + 3 = \boxed{\ln(x^3) + 3}$