The constant multiple rule states that when a function is multiplied by a constant, you can simply “pull out” the constant, apply the mathematical operation (derivative or integral) to the function, and then multiply the result by the constant.
The derivative of a constant c times a function f(x) is the constant times the derivative of the function:
![\frac{d}{dx}\left[ c\cdot f\left( x \right) \right] \,\,=\,\,c\,\,\cdot \,\,f\prime\left( x \right)](https://s0.wp.com/latex.php?latex=%5Cfrac%7Bd%7D%7Bdx%7D%5Cleft%5B+c%5Ccdot+f%5Cleft%28+x+%5Cright%29+%5Cright%5D+%5C%2C%5C%2C%3D%5C%2C%5C%2Cc%5C%2C%5C%2C%5Ccdot+%5C%2C%5C%2Cf%5Cprime%5Cleft%28+x+%5Cright%29&bg=ffffff&fg=666666&s=3&c=20201002)
References
“Constant Multiple Rule.” GeeksforGeeks, July 23, 2024. https://www.geeksforgeeks.org/maths/constant-multiple-rule/.
“Constant Multiple Rule – Formula, Proof, Examples, Application.” CUEMATH. Accessed June 30, 2026. https://www.cuemath.com/calculus/constant-multiple-rule/.
Ming, Albert. “7 Derivative Rules You Should Know.” Medium, April 19, 2021. https://albertming88.medium.com/7-derivative-rules-you-should-know-ce405b8f9f4d.