n'
f(x)
f'(x) or dy/dx
d/dy
A derivative represents the rate at which a function is changing at any given point.
It is the area under a curve.
It refers to a function being constant.
An average rate of change of two points.
The average slope between two points.
It indicates the slope of the tangent line at any point on the function's graph.
The height of the graph.
The horizontal shift of the graph.
The derivative of a constant function is always zero.
It is equal to the value of the constant.
It varies depending on the function.
It is always infinity.
If f(x) = x^n, the derivative f'(x) = n*x^2.
x^(n-1) becomes 0.
If f(x) = x^n, the derivative f'(x) = n*x^(n-1).
The nth derivative is simply x^1.
x^2
4x
x^3
2x
3x^2
6x^2
12x^3
9x^2
They are only applicable in discrete functions.
Higher order derivatives result in constant values.
Higher order derivatives are derivatives of derivatives, such as the second derivative, third derivative, etc.
They involve only linear equations.
The speed of the function.
The highest point of the function.
It provides information about the function's concavity and points of inflection.
The lowest point of the function.
A method for integrating functions.
The Chain Rule is a formula to compute the derivative of a composite function.
Derives the sum of two functions.
Applies only to polynomial functions.
The derivative of a position function with respect to time is the velocity.
It determines distance moved over time.
It is not related to velocity.
It directly gives the acceleration.
3
5
x
It has no derivative.
It means the function is increasing at that point.
The function is constant.
The function is decreasing.
It signifies a maximum point.
It means the function is having a discontinuity.
It means the function is decreasing at that point.
The derivative has reached zero.
It means the function is increasing.
They are primarily academic and have no real application.
They are used only for graphing purposes.
They help in determining static positions.
They are used to calculate rates of change in various fields like physics, engineering, economics, etc.