Beginners Calculus and derivatives

Question

Hi, I new to Calculus and am trying to understand how the various rules have been applied to the following questions, in order to arrive at the answers. I am familiar with the power, sum, product rules etc, but cant fully understand how they have been applied here. Thank you in advance.

In the following equations, a and b are constants, and E is a function of the variable t .Find expressions for ݀dx/dt in terms of a,b,E and dE/dt.

x = aE + b

Answer dx/dt = aE dE/dt

x = a exp (-bE)

Answer dx/dt = -ab exp (-bE) dE/dt

Answer 1

(1)

The answer provided to question 1 is not correct.

x(t) = aE(t) + b

dx/dt = a dE/dt

(2)

x = a e^-bE(t)

Use the chain rule for this one.

dx/dt = a e^-bE(t) (-b dE/dt)