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Home  Differentiation Derivatives of Rational Functions Theorem 3: Constant Rule |
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Theorem 3: Constant Rule
THEOREM 3 (Constant Rule) Suppose u depends on x, and c is a real number. Then for any value of x where du/dx exists,
PROOF Let y = cu, and let Δx ≠ 0 be infinitesimal. Then
Taking standard parts,
whence
The Constant Rule shows that in computing derivatives, a constant factor may be moved "outside" the derivative. It can only be used when c is a constant. For products of two functions of x, we have:
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Last Update: 2010-11-25