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Reference.org
Linearity of differentiation
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<p>In <a href="/facts/Calculus/MEmUTYoz">calculus</a>, the <a href="/facts/Derivative/7Ito70Dh">derivative</a> of any <a href="/facts/Linear_combination/CVjL6kuN">linear combination</a> of <a href="/facts/Function_(mathematics)/CdReEKCh">functions</a> equals the same linear combination of the derivatives of the functions; this property is known as linearity of differentiation, the rule of linearity, or the <a href="/facts/Superposition_principle/GKGs9C92">superposition rule</a> for differentiation. It is a fundamental property of the derivative that encapsulates in a single rule two simpler rules of differentiation, the <a href="/facts/Sum_rule_in_differentiation/9q1b7Ev6">sum rule</a> (the derivative of the sum of two functions is the sum of the derivatives) and the <a href="/facts/Constant_factor_rule_in_differentiation/9q1b7Ev6">constant factor rule</a> (the derivative of a constant multiple of a function is the same constant multiple of the derivative). Thus it can be said that differentiation is <a href="/facts/Linear_map/Q1PBKNVV">linear</a>, or the <a href="/facts/Differential_operator/Nr15J0IE">differential operator</a> is a <a href="/facts/Linear_map/Q1PBKNVV">linear</a> operator. </p>