Question

Find the dy/dx for the equation below using implicit differentiation. Tq

Answer 1

The derivative of an exponential function is

$\dfrac{d}{dx} a^x = a^x\log(a)$

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

$\dfrac{d}{dx} 3^{-x} = 3^{-x}\log(3)\cdot (-1)=-3^{-x}\log(3)$