Find the derivative of the function

Question

Find the derivative of the function.

g(x) = 400(1 − e^−0.1x)

Answer 1

g(x) = 400 - 400 exp(-0.1x); note that g(0) =0

g'(x) = 400 *-0.1 exp(-0.1x) = -40 exp(-0.1x)

checks by integration:

anti-derivative is -40 exp(-0.1x)/-0.1 + c = G(x)

since g(0)=0 ---> -40 exp(-0.1*0)/0.1 + c = 0

-400 + c = 0

c=400

the function is g(x) = -40exp(-0.1x)/0.1 + 400

400 - 40/0.1 exp(-0.1x)

400 - 400 exp(-0.1x)

which is the original function

Therefore the derivative is correct!!!

-40 exp(-0.1x)