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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.

### Definition of Derivative:

The following formulas give the Definition of Derivative. Scroll down the page for more examples and solutions.

### Interpretation of the Derivative as the Slope of a Tangent

### Derivative Notations

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*) = *x*^{2}

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More Lessons for Calculus

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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 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.

*Example: *

Use the derivative to find the slope at any point along the following curves.

a) *f*(*x*) = 2*x*^{2}

b) *f*(*x*) =

*Solution: *

a) *f*(*x*) = 2*x*^{2}

b)

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
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