what will i get if i diffferentiate the following exponential function? exp -[sqrt (0.001t)]?

Answer 1

F(x) = exp(-x)
G(t) = x = sqrt(0.001t)

The given function is F(G(t)). By the chain rule, the derivative with respect to t is F'(G(t))*G'(t)
G'(t) = derivative of x = 0.001/2sqrt(0.001t).
F'(x) = -exp(-x)
F'(G(t)) = -exp(-G(t)) = -exp(-sqrt(0.001t))

So The derivative required is the product
-0.001exp(-sqrt(0.001t)divided by
[2sqrt(0.001t)])

Answer 2

you get -exp[-sqrt(.001t)]*.001

divided by [2*sqrt(.001t)]

used the chain rule twice

Answer 3

1/(2000sqrt.001t)