Constant multiple rule

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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:

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