How To Find Derivative Of A Graph | Easiest Method

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How To Find Derivative Of A Graph

If you are a science stream guy, then derivative has become a part of your daily routine most probably. As you start studying mathematics, physics, and chemistry in high school, immediately you get introduced to this significant agent of mathematics, then if you plan to continue your studies in technology area possibly in engineering. The derivatives especially to find derivative of a graph is something which you will explore in this article and it will be mixed up with your soul permanently.

Whether it be physics or chemistry, applications of derivatives and to find derivative of a graph is everywhere. Most of the times, derivative are closely related to the graphs. It is possible to calculate the derivative of a function from its plot. The result of a derivative calculated from a graph may not have the same accuracy as calculated from an original equation. But you can surely have an idea of the rate of change of the function from the derivative of the graph.

What is a Derivative?

A derivative an implement of calculus which is a part of mathematics. It is a regular requisition for estimating several aspects of science. A derivative generally represents the rate of change of a given function. When you change the input of a particular function, the output also changes gradually. This scenario is represented by the derivative.

tangent of a graph
tangent of a graph

A function consists of an input and an output segment. The derivative helps in establishing the relation of improvement between them. It shows the dependency of the output of the function on the input section. It can be shown manually. There is a lot of software also available to determine the derivative of a function.

Application of Derivatives

If you are from a science background, you must know the solemnity of derivative in the field of science. It may be the formula of velocity or the reaction rate of a chemical experiment. One can use derivatives to show the result mathematically. There is more utilization of derivatives in the domain of science and technology.

The applications are:

  • In physics, the derivative is used to estimate the rate of change. For example, the change of distance with respect to time or the rate of change of speed with the respect of time is known as velocity and acceleration, respectively. This particular can also be analyzed if one is able to find derivative of a graph.

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    Physics: Applications of derivatives
  • In order to obtain critical points of a function, it’s crucial to find derivative of a graph.
  • From the derivative of a graph, one can also obtain the maximum and minimum value of a function.
  • We may use the derivative of a graph in the linear approximations in specific points of a function.
  • A derivative is also in use with several theorems and formulae like mean value theorem, L’ Hospital rule, and Rolle’s theorem.

Steps to Find Derivative Of A Graph

To find derivative of a graph, you need to follow these steps:

Selection of the appropriate point for derivative

At first, you have to choose a suitable point on your curve for estimation of the derivative. The selected point will show the slope of the graph on itself. As derivative indicates the gradient of the plotting, so it will change on each and every point of the curve.

Draw a Tangent on the Chosen point

After picking up the point on the graph, you have to go for the tangent representation on the point. The tangent is a straight line, and it must be touched on a single point on the curve, it will evince the accuracy of the curve. However, it is a tiresome and tough action to perform the gradient line determination.

Tangents at multiple points
Tangents at multiple points of a curve

The more the line touches on a single point, the more is the accuracy of the tangent. You may extend the straight line of the slope as long as the curve allows you to do so, but you should note the horizontal and vertical coordinate values simultaneously. More than half of your work is complete as soon as you finish drawing the tangent correctly.

Determination of Derivative from the Tangent

After illustrating the gradient line accurately, you have to put on record the X and Y axis coordinate values of the gradient line in order to find derivative of a graph. The values will indicate the position of the start and end point of the tangent line. Right after acquiring the coordinate values, you can estimate the derivative of the plot on that particular point. To compute it follow the following steps:

A derivative of the graph on a particular point = (The difference between Y-axis coordinate values of tangent) / (The difference between X-axis coordinate values of tangent)

As the coordinate values of the slope are the governing framework of derivate calculation, so it is easy to interpret that the derivative will change from point to point on the graph. Thus a derivative can indicate the rate of change of a function.

Roadmap to Find Derivative Of A Graph Accurately

To find derivative of a graph ideally, you have to draw the tangent line precisely first.

  • Use a sharp headed pencil to draw the gradient line on the curve.
  • You should use a straight and sharp-edged ruler to draw the tangent.
  • The ruler must be in alignment on a single point on the curve. Only thus, you can get the gradient line in orientation on a specific point.
  • Mark the coordinates of the tangent line perfectly.

Following the above steps, you can find derivative of a graph on the selected point.

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