Question

Given f(x)= a×e−bx , where a = 1 and b = 6,

calculate g(x)=dfdx and obtain g(1) (that is, evaluate the derivative of f(x) at x = 1).
Report your answer with three significant figures.

Answer 1

g(1) = -0.015

Explanation:

We are given he following in the question:

`f(x) = ae^(-bx)`

For a = 1 and b = 6, we have,

`f(x) = e^(-6x)`

We have to find the the derivative of f(x) with respect to x.

`g(x) = (d(f(x)))/(dx) = (d(e^(-6x)))/(dx)\\\\g(x) = -6e^(-6x)\\\\g(1) = (d(f(x)))/(dx)\bigg|_(x=1) = -6e^(-6) = -0.015`

Thus, g(1) = -0.015