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Derivative of a constantThe derivative of any constant is zero. This can be easily conceptualized if you think of the graph of any constant value.

The derivative can be thought of as the slope of the line tangent to a curve at any given point. If you graph the expression y = 3, for example, it is just a horizontal line intercepting the y axis at 3. The slope of that line is, of course, equal to zero, for any point on the curve (which in this case is a straight line). Therefore, the derivative (with respect to x) of y = 3 is zero. Since the slope of any horizontal line is zero, the derivative of any line of the form y = k, where k is a constant, is zero.


Any constant quantity and an expression that has a maximum or minimum or both, has a derivative equal to zero.

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Q: What quantity or expression has a derivative equal to zero?
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