Question

question 8 - 1 point what is the first derivative of f(x)=-9(e^x)^(-2). select the correct answer below: f(x)=-9e^(-2x) f(x)=18e^(-3x) f(x)=9/2e^(-2x) f(x)=18e^(-2x)

Explanation:

Step1: Rewrite function

$f(x)=-9(e^{x})^{-2}=-9e^{-2x}$

Step2: Apply derivative rule

If $y = ae^{bx}$, then $y'=abe^{bx}$. Here $a = - 9$, $b=-2$, so $f'(x)=(-9)\times(-2)e^{-2x}=18e^{-2x}$

Answer:

$f'(x)=18e^{-2x}$