Question

Derivadas de primeira da funções:

f(x) = (3x elevado a 2 +1). e elevado a x

f(x) = x elevado a 2 - 4 / x

Answer 1

$f(x)=u(x)\cdot v(x)\to f'(x)=u'(x)\cdot v(x)+u(x)\cdot v'(x)\\\\f(x)=\dfrac{u(x)}{v(x)}\to f'(x)=\dfrac{u'(x)\cdot v(x)-u(x)\cdot v'(x)}{v(x)^2} \\\\\\a)\ u(x)=3x^2+1\to u'(x)=6x\\\\\ v(x)=e^x\to v'(x)=e^x\\\\f'(x)=(6x)(e^x)+(3x^2+1)(e^x)=e^x(3x^2+6x+1)\\\\\\b)\ u(x)=x^2-4\to u'(x)=2x\\\\\ v(x)=x\to v'(x)=1\\\\f'(x)=\dfrac{(2x)(x)-(1)(x^2-4)}{x^2}=\dfrac{x^2+4}{x^2}$