Answer:
The first derivative of the given function
[tex]\frac{df(x)}{dx} = - ab e^{-b x}[/tex]
Step-by-step explanation:
Step(i):-
Given f(x) = ae⁻ᵇˣ ...( i )
we will use differentiation formula
[tex]\frac{d(e^{ax}) }{dx} = a e^{a x}[/tex]
Step(ii)
Differentiating equation (i) with respective to 'x', we get
[tex]\frac{df(x)}{dx} = a e^{-b x} \frac{d}{dx} (-b x )[/tex]
= -ab e⁻ᵇˣ
[tex]\frac{df(x)}{dx} = - ab e^{-b x}[/tex]
Final answer:-
The first derivative of the given function
[tex]\frac{df(x)}{dx} = - ab e^{-b x}[/tex]
