product rule and differentiate natural log function
= 3^x * ln(x) )
= (3^x)' (ln(x)) + (3^x) (ln(x))' )
= (3^xln3)(ln(x)) + (3^x)(\frac{1}{x}) )
= (3^xln3)(ln(x)) + \frac{3^x}{x} )
\\can be simplified or stop here?
Re: product rule and differentiate natural log function
Quote:
Originally Posted by
rabert1 
No. Just stop. But to be strictly correct it should be )
. It is a function.
Re: product rule and differentiate natural log function
Alternative form :
=3^x \cdot \ln x^{\ln 3}+3^x \cdot \ln e^{\frac{1}{x}}=3^x \cdot \ln \left(x^{\ln 3} \cdot e^{\frac{1}{x}}\right))
