Derivative of a constant. In calculus, the derivative of a constant function is zero (A constant function is one that does not depend on the independent variable, such as f(x) = 7).The rule can be justified in various ways. The derivative is the slope of the tangent to the given function\'s graph, and the graph of a constant function is a horizontal line, whose slope is zero.ProofA formal proof, from the definition of a derivative, is:In Leibniz notation, it is written as:.

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