Question

derivada das funções:f(x)= (3x 1/x) . (6x -1) 

Answer 1

$\displaystyle f(x)=\underbrace{\big(\frac{3x\pm1}{x}\big)}.\underbrace{\big(6x-1\big)}\\.\ \ \ \ \ \ \ \ \ \ \ u(x)\ \ \ \ v(x)\\\\\frac{df}{dx}=\frac{du}{dx}v(x)+\frac{dv}{dx}u(x)\\\\\\i)\frac{du}{dx}=\frac{3(x)-3x\pm1}{x^2}=\pm\frac{1}{x^2}\\\\ii)\frac{dv}{dx}=6\\\\iii)\frac{df}{dx}=\pm\frac{1}{x^2}.(6x-1)+\frac{3x\pm1}{x}.6\implies \frac{df}{dx}=\underline{\pm\frac{6x-1}{x^2}+\frac{18x\pm6}{x}}$