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qwelly [4]
3 years ago
7

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

Mathematics
1 answer:
11Alexandr11 [23.1K]3 years ago
7 0

Answer:

The first derivative of the given function

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

Step-by-step explanation:

<u><em>Step(i):-</em></u>

Given f(x) = ae⁻ᵇˣ  ...( i )

we will use differentiation formula

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

<em><u>Step(ii)</u></em>

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}

<u><em>Final answer:-</em></u>

The first derivative of the given function

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

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