The study of differential calculus is concerned with how one quantity changes in relation to another quantity. The central concept of differential calculus is the derivative.
The following formulas give the Definition of Derivative. Scroll down the page for more examples and solutions.
The tangent line to y = f(x) at (a,f(a)) is the line through (a, f(a)) whose slope is equal to f’(a), the derivative of f at a. This means that the derivative is the slope of a curve at a given point on the curve.
Use the derivative to find the slope at any point along the following curves.
a) f(x) = 2x2
b) f(x) =
a) f(x) = 2x2
If we use the traditional notation y = f(x) to indicate that the independent variable is x and the dependent variable is y, then some common notations for the derivatives are as follows:
What is a derivative?
Understanding the Definition of the Derivative
The following video shows how to find the slope of a tangent line to a curve and gives the definition of a derivative.
The following video shows how to use the derivative to find the slope at any point along f(x) = x2
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