Respuesta :

The derivative of an exponential function is

[tex]\dfrac{d}{dx} a^x = a^x\log(a)[/tex]

Moreover, in this case we must apply the chain rule because the exponent is -x:

[tex]\dfrac{d}{dx} 3^{-x} = 3^{-x}\log(3)\cdot (-1)=-3^{-x}\log(3)[/tex]