When to use the power rule or the chain rule?

You'd use the power rule for something like 2x^3 because its only a coefficient times a variable with a number being an exponent. So you'd use the power rule for anything that looks like, x^n  and n being a (natural) number.

You would use a chain rule for something that looks like e^x or sin(x) or cos(x) or anything that has a function within a function. So the derivative of these equation would be the derivative of the outer function (keeping the inner function the same) times the derivative of the inner function.

good luck!

You must use the chain rule when whenever the function in question is a composition of functions.

But you know what the interesting thing is? You are actually doing chain rule even when you do the power rule. The power rule is just a generalization of the chain rule to differentiation of monomials raised to a power. For instance:

When you apply chain rule, you multiply the derivative of the inside function by the derivative of the inside function. The inside function in this case is just x

d/dx(2x^3) = (3)(2)x^2(x')

When you differentiate with respect to x, x' is just 1.

d/dx(e^-10x) = (-10x)'e^-10x = -10e^-10x