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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.

Answer2:

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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The derivative of ANY constant expression - one that doesn't depend on variables - is zero.

you have to first find the derivative of the original function. You then make the derivative equal to zero and solve for x.

A quantity which does not equal zero is said to be nonzero.

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This means that the function has reached a local maximum or minimum. Since the graph of the derivative crosses the x-axis, then this means the derivative is zero at the point of intersection. When a derivative is equal to zero then the function has reached a "flat" spot for that instant. If the graph of the derivative crosses from positive x to negative x, then this indicates a local maximum. Likewise, if the graph of the derivative crosses from negative x to positive x then this indicates a local minimum.

Related questions

The derivative of ANY constant expression - one that doesn't depend on variables - is zero.

The derivative of any constant - any expression that does not involve the independent variable - is zero.

When the numerator of any expression or fraction is zero then the result is zero because zero divided by any number is always equal to zero.

you have to first find the derivative of the original function. You then make the derivative equal to zero and solve for x.

When the first derivative of the function is equal to zero and the second derivative is positive.

The derivative of 40 is zero. The derivative of any constant is zero.

A quantity which does not equal zero is said to be nonzero.

Continuity in mathematics is the first derivative equal to zero or the Boundary condition.

A nonzero whole number is a quantity which does not equal zero and number without fractions.

You do not. If you do, the expression is undefined: it has no value.

It cannot be zero.

zero. In this problem, since there is no variable, the derivative is zero.

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