Question

preciso de ajuda nisso aqui
derive
x*senx/1+x

Answer 1

Derivada de sen(x)=cos(x)

regra do produto = f'(x)g(x)+g'(x)f(x)

regra do quociente = $\frac{f'(x)g(x)-g'(x)f(x)}{(g(x))^{2} }$

$\boxed{x*\frac{sen(x)}{1+x}}\\\boxed{\frac{sen(x)}{1+x}' = \frac{cos(x)(1+x)-1(sen(x))}{(1+x)^{2} } } \\\frac{d}{dx} \boxed{x* \frac{sen(x)}{1+x}} =\\1(\frac{sen(x)}{1+x})+x(\frac{cos(x)(1+x)-1(sen(x))}{(1+x)^{2} } )\\\frac{sen(x)}{1+x}+\frac{x(cos(x)(1+x)-sen(x))}{(1+x)^{2} }\\\frac{sen(x)(1+x)+x(cos(x)(1+x)-sen(x))}{(1+x)^{2} } \\\frac{sen(x)+xsen(x)+xcos(x)+x^{2}cos(x)-xsen(x)}{(1+x)^{2} } }\\\boxed{\frac{x^{2} cos(x)+xcos(x)+sen(x)}{(1+x)^{2} } }$