Math Calcs Derivative calculator is a online calculator to calculate the derivative of a function. The function can be algebraic, trigonometric, hyperbolic function, polynomial, exponential, logarithmic, inverse hyperbolic function.

Our calculator can parse any type of function and calculate the derivative of the function using the rules of differentiation. If you want to view the step by step solutions, just click show steps and you will see every steps

The Derivative also called Differential Calculus, of a function is an instantaneous rate of change of the function at a point. More formally, derivative is a fundamental concept of the calculus to measure how the value of the function changes with respect to the input of that function.

Derivative is not a theoritical concepts, it has manty real world applications. Its not only limited to engineering, but in economics, and even biology as well.

Any subject that deals with change over time, uses derivative to measure that change at a point.

There is no single hand in the development of the concept of the Differential Calculus or Derivative.

Many mathematicians have contributed and devised the concept of the derivative. It was not developed by single person or in a single time, but have been developed over time by many mathematicians.

The first person to introduce the concept of derivative was Gottfried Wilhelm Leibniz’s 1684 paper Nova methodus pro maximis et minimis, itemque tangentibus, quae nec fractas nec irrationales, quantitates moratur, et singulare pro illi calculi genus (A New Method for Maxima and Minima as Well as Tangents, Which is Impeded Neither by Fractional Nor by Irrational Quantities, and a Remarkable Type of Calculus for This).

Derivative can be defined as the slope of the tangent line at a point on a graph of that function. So, we can say derivative is the instantaneous slope

We need to understand slope to understand the derivative, but not the other way around.

The concept of slope is taught in early stages education, but derivative is taught in higher education, cause its a it complex concept than slope

To calculate the derivative of a function (rate of change of a function at a point), you have to find the slop of a function. As simple as that, because slope represents the rate of change at a point.

There are different rules to calculate the differentiation/derivative of a function. The common rules you will use a lot is product rule.

There are other as well such as: Chain Rule, Quotient Rule, Power Rule, Exponential Rule, Logarithmic Rule, Trigonometric Rule, etc. Each of these rules have specific use cases.

For example, The Trigonometry rule is used when dealing with trigonometric functions like Sin, Cos, Tan, Sec, etc

As we said earlier, the derivative is a instantaneous rate of change. But what does that mean?

Because a change is measured between two points, but the instant change in a point is not possible to measure, because there is not room for change at any instant without comparing it with another point