In calculus, the constant factor rule in differentiation allows one to take constants outside a derivative and concentrate on differentiating the function of x itself. This is a part of the linearity of differentiation.
Consider a differentiable function
where k is a constant.
Use the formula for differentiation from first principles to obtain:
This is the statement of the constant factor rule in differentiation, in Lagrange's notation for differentiation.
In Leibniz's notation, this reads
If we put k = −1 in the constant factor rule for differentiation, we have:
1 : Differentiation rules
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