Question

What is the first derivative of the following function: f(x) = aexp(-bx)

Answer 1

Answer:

The first derivative of the given function

$\frac{df(x)}{dx} = - ab e^{-b x}$

Step-by-step explanation:

Step(i):-

Given f(x) = ae⁻ᵇˣ  ...( i )

we will use differentiation formula

$\frac{d(e^{ax}) }{dx} = a e^{a x}$

Step(ii)

Differentiating equation (i) with respective to 'x', we get

$\frac{df(x)}{dx} = a e^{-b x} \frac{d}{dx} (-b x )$

       = -ab e⁻ᵇˣ

$\frac{df(x)}{dx} = - ab e^{-b x}$

Final answer:-

The first derivative of the given function

$\frac{df(x)}{dx} = - ab e^{-b x}$