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.

Apply the sum/difference rule and constant multiple rule: $f'(x) = 6x + 5$.

Apply the constant rule: $f'(x) = 0$.

Apply the sum/difference rule and constant multiple rule: $f'(x) = 12x^2 - 2$.

Apply the sum rule, constant rule, and constant multiple rule: $f'(x) = 20x^3$.

Apply the difference rule and constant multiple rule: $f'(x) = 4x - 6$.

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 $f'(x) = c cdot g'(x)$.