Question

f(x) = 3 x^(2)ln x
what is f'(x)=
andf'(e^4)=

Answer 1

find the 1st derivative using the product rule

u 3x^2 u' = 6x

v = ln(x) v' = 1/x

so

\[f'(x) = u \times v' + v \times u'\]

substitute and simplify...

the 2nd part is the substitute

\[x = e^4\] into the derivative above.

hope this helps

Answer 2

f'(x)= \[3x(1+ 2\ln x )\]

f'(e^4)= \[27e ^{4}\]

Answer 3

thanks :)