Pranuler
Pranuler Pranuler
  • 19-04-2017
  • Mathematics
contestada

hey guys, real fast


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

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TSO
TSO TSO
  • 19-04-2017
You will need to use product rule.
The product rule is:
[tex]\frac{d}{dx}[f(x)g(x)] = f'(x)g(x)+f(x)g'(x)[/tex]


[tex]\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[/tex]

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