If $f(x) = c$, then $f'(x) = 0$.

If $f(x) = g(x) + h(x)$, then $f'(x) = g'(x) + h'(x)$.

If $f(x) = g(x) - h(x)$, then $f'(x) = g'(x) - h'(x)$.

If $f(x) = c cdot g(x)$, then $f'(x) = c cdot g'(x)$.

The instantaneous rate of change of a function.

A fixed value that does not change.

The derivative of a sum of functions is the sum of their derivatives.

The derivative of a difference of functions is the difference of their derivatives.

The derivative of a constant times a function is the constant times the derivative of the function.

The derivative of a constant is always zero because a constant's value does not change.

When differentiating a sum of functions, you can differentiate each function separately and then add the results.

When differentiating a difference of functions, you can differentiate each function separately and then subtract the results.

A constant multiplying a function remains as a multiplier when you take the derivative of the function.