Question

Quanto vale a Derivação da função f(x)=sen(x²+3x-5) ?

Answer 1

$\frac{df(x)}{dx}~=~\left(~sen(x^2+3x-5)~\right)'\\\\\\Vamos~utilizar~a~regra~da~cadeia.\\\\Seja:~u~=~x^2+3x-5\\\\\frac{df(x)}{dx}~=~\left(~sen(u(x))~\right)'\\\\\\\frac{df(x)}{dx}~=~\frac{df(u)}{du}~.~\frac{du(x)}{dx}\\\\\\\frac{df(x)}{dx}~=~(~sen(u(x))~)'~.~(~u(x)~)'\\\\\\\frac{df(x)}{dx}~=~cos(u(x))~.~(~x^2+3x-5~)'\\\\\\\frac{df(x)}{dx}~=~cos(u(x))~.~(2x+3)\\\\\\\boxed{\frac{df(x)}{dx}~=~(2x+3)\,.\,cos(x^2+3x-5)}$