Question

derivar 2 e elevado há potência 3x²+6x+7

Answer 1

$f(x)~=~2^{3x^2+6x+7}\\\\\\\frac{df(x)}{dx}~=~\left(2^{3x^2+6x+7}\right)'\\\\\\Utilizando~a~regra~da~cadeia\\\\Seja:~u(x)~=~3x^2+6x+7\\\\\\\frac{df(x)}{dx}~=~\frac{df(u)}{du}.\frac{du(x)}{dx}\\\\\\\frac{df(x)}{dx}~=~\left(2^u\right)'.\,(3x^2+6x+7)'\\\\\\\frac{df(x)}{dx}~=~\left(~2^u.ln(2)~\right).\,(3~.~2x^1+6)\\\\\\\frac{df(x)}{dx}~=~\left(~2^{(3x^2+6x+7)}.ln(2)~\right).\,(6x+6)\\\\\\\boxed{\frac{df(x)}{dx}~=~ln(2)~.~(6x+6)~.~2^{(3x^2+6x+7)}}$