# Derivative - History And Usefulness, The Basic Concept, A Concrete Example

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curve called mathematics process

In **mathematics**, the derivative is the exact **rate** at which one quantity changes with respect to another. Geometrically, the derivative is the slope of a **curve** at a **point** on the curve, defined as the slope of the tangent to the curve at the same point. The process of finding the derivative is called differentiation. This process is central to the branch of mathematics called differential **calculus**.

**Figure 1.** Illustration by Hans & Cassidy. Courtesy of Gale Group.

## Additional Topics

Calculus was first invented by Sir Isaac Newton around 1665. Newton was a physicist as well as a mathematician. He found that the mathematics of his time was not sufficient to solve the problems he was interested in, so he invented new mathematics. About the same time another mathematician, Goltfried Leibnez, developed the same ideas as Newton. Newton was interested in calculating the velocity of …

The derivative is often called the "instantaneous" rate of change. A rate of change is simply a comparison of the change in one quantity to the simultaneous change in a second quantity. For instance, the amount of money your employer owes you compared to the length of time you worked for him determines your rate of pay. The comparison is made in the form of a ratio, dividing the chan…

A fairly simple, and not altogether impractical example is that of the falling apple. Observation tells us that the apple's initial speed (the instant before letting go from the tree) is zero, and that it accelerates rapidly. Scientists have found, from repeated measurements with
Figure 3. Illustration by Hans & Cassidy. Courtesy of Gale Group.
various falling objects (neglectin…

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## User Comments

almost 3 years ago

i need a short and complete history of derivatives

about 3 years ago

mathematics

over 2 years ago

very nice

8 months ago

Jason

Thanks for sharing. Derivatives are indeed very useful in mathematics. http://www.uniqueessays.com

over 1 year ago

SRINIVASAN PT

images are not available... please resolve it...