Question

Resolva a derivada:

f(x)= x^2Inx + 2e^x

Answer 1

Boa tarde Ariely!

Solução!

$f(x)= x^{2}lnx +2e^x\\\\\\ f(x)= x^{2} .lnx+2e^x\\\\\\\ Novamente!\\\\\\\ u= x^{2} ~~~~~v=lnx\\\\\\ u'=2x~~~~~~v'= \dfrac{1}{x}\\\\\\\ Derivada~~de~~2e^x=2e^x$

$f'(x)= x^{2} . \dfrac{1}{x}+2x.lnx+2e^x\\\\\\\\ f'(x)=\dfrac{ x^{2} }{x}+2x.lnx+2e^x\\\\\\\\ f'(x)=x+2x.lnx+2e^x\\\\\\\\\\ \boxed{Resposta:f'(x)=x+2x.lnx+2e^x}$

Boa tarde!
Bons estudos!