โˆซcalculus i review

key term - Constant Multiple Rule

Definition

The Constant Multiple Rule states that the derivative of a constant multiplied by a function is the constant multiplied by the derivative of the function. Mathematically, if $c$ is a constant and $f(x)$ is a differentiable function, then $(cf(x))' = c f'(x)$.

5 Must Know Facts For Your Next Test

  1. The Constant Multiple Rule can be expressed as $(cf(x))' = c f'(x)$ where $c$ is a constant.
  2. This rule simplifies differentiation when functions are scaled by constants.
  3. It applies to both polynomial and non-polynomial functions as long as they are differentiable.
  4. Combining this rule with other differentiation rules like the Product Rule or Chain Rule can simplify complex derivatives.
  5. If $f(x) = x^n$, then applying the Constant Multiple Rule gives $(cx^n)' = c(nx^{n-1})$.

Review Questions

"Constant Multiple Rule" also found in: