Question

Determine as seguintes derivadas : d) Y= x.ln(2x+1)

Answer 1

$\displaystyle \sf y = x\cdot ln(2x+1) \\\\ \underline{derivando}: \\\\ y' = (x)'\cdot ln(2x+1)+x\cdot[\ ln(2x+1)\ ]' \\\\ y' = 1\cdot ln(2x+1)+x\cdot \frac{(2x+1)'}{(2x+1)} \\\\ y' = ln(2x+1)+x\cdot \frac{2}{(2x+1)} \\\\\\ \boxed{\sf y' = ln(2x+1)+\frac{2x}{(2x+1)} }$