Question

Qual a derivada de 9x(Lnx)?

Answer 1

Utilizando o método da multiplicação:

$\frac{\partial \left(~9x(lnx)~\right)}{\partial x}=(9x)'~.~lnx~+~(lnx)'~.~9x\\\\\\\frac{\partial \left(~9x(lnx)~\right)}{\partial x}=9~.~lnx~+~\frac{1}{x}~.~9x\\\\\\\boxed{\frac{\partial \left(~9x(lnx)~\right)}{\partial x}~=~9lnx~+~9}$

Answer 2

$\sf f(x)=9x(\ell n(x))\\\sf f'(x)=9\cdot\ell n(x)+9\diagup\!\!\!x\cdot\dfrac{1}{\diagup\!\!\!x}=9\cdot(\ell n(x)+1)$