If you mean "what is the deriviative of f(x) = 0?", the answer is 0. (zero) The deriviative of any constant is zero.
Yes.
The rate of change of any function is its derivative. The equation of a horizontal line is simply a constant, for example y=10. The derivative of any constant is ZERO.
You take the derivative of the function. The derivative is another function that tells you the slope of the original function at any point. (If you don't know about derivatives already, you can learn the details on how to calculate in a calculus textbook. Or read the Wikipedia article for a brief introduction.) Once you have the derivative, you solve it for zero (derivative = 0). Any local maximum or minimum either has a derivative of zero, has no defined derivative, or is a border point (on the border of the interval you are considering). Now, as to the intervals where the function increase or decreases: Between any such maximum or minimum points, you take any random point and check whether the derivative is positive or negative. If it is positive, the function is increasing.
Usually at the minimum or maximum of a function, one of the following conditions arises:The derivative is zero.The derivative is undefined.The point is at the end-points of the domain that is being considered (or of the naturally-defined domain, for example, zero for the square root).This will give you "candidate points"; to find out whether each of these candidate points actually is a maximum or a minimum, additional analysis is required. For example, if the second derivative is positive, you have a minimum, if the second derivative is negative, you have a maximum - but if it is zero, it may be a maximum, a minimum, or neither.
The derivative of 40 is zero. The derivative of any constant is zero.
zero. In this problem, since there is no variable, the derivative is zero.
Zero. In general, the derivative of any constant is zero.
The "double prime", or second derivative of y = 5x, equals zero. The first derivative is 5, a constant. Since the derivative of any constant is zero, the derivative of 5 is zero.
At the point of inflexion:the first derivative must be zero. the second derivative must be zero, if the next derivative is zero then the one following that must also be zero.
zero
The derivative of sqrt(2) is zero.
the second derivative at an inflectiion point is zero
zero
you have to first find the derivative of the original function. You then make the derivative equal to zero and solve for x.
ln(3) is a constant. If graphed, it would be a horizontal line. Its derivative is zero.
coz there is sex