Derivatives are usually taken with respect to time. The first derivative would have units of volume / time, i.e., a flow - for example - "so-and-so many cubic meters per second flow down our river".
The second derivate would refer to a change in the flow - when the flow of a liquid or gas increases or decreases with time.
the second derivative at an inflectiion point is zero
When the first derivative of the function is equal to zero and the second derivative is positive.
You are supposed to use the chain rule for this. First step: derivative of root of sin2x is (1 / (2 root of sin 2x)) times the derivative of sin 2x. Second step: derivative of sin 2x is cos 2x times the derivative of 2x. Third step: derivative of 2x is 2. Finally, you need to multiply all the parts together.
(x3)'=3x2(x3)''=(3x2)'=6x
she thought she would get points of infliction!
The Geometrical meaning of the second derivative is the curvature of the function. If the function has zero second derivative it is straight or flat.
All it means to take the second derivative is to take the derivative of a function twice. For example, say you start with the function y=x2+2x The first derivative would be 2x+2 But when you take the derivative the first derivative you get the second derivative which would be 2
The first derivative is the rate of change, and the second derivative is the rate of change of the rate of change.
well, the second derivative is the derivative of the first derivative. so, the 2nd derivative of a function's indefinite integral is the derivative of the derivative of the function's indefinite integral. the derivative of a function's indefinite integral is the function, so the 2nd derivative of a function's indefinite integral is the derivative of the function.
A derivative is to the rate of change asan integral is to area/volume.
2x is the first derivative of x2.
2x is the first derivative of x2.
Yes.
Afetr you take the first derivative you take it again Example y = x^2 dy/dx = 2x ( first derivative) d2y/dx2 = 2 ( second derivative)
the second derivative at an inflectiion point is zero
No. A quadratic equation always has a second derivative that is a constant. For example -3x2 + 10x - 2 first derivative -6x + 10 second derivative -6
The same way you get the second derivative from any function. Assuming you have a function that expresses potential energy as a function of time, or perhaps as a function of position, you take the derivate of this function. This will give you another function. Then, you take the derivate of this derivative, to get the second derivative.