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## Calculus – Derivatives

The derivative is a central concept in calculus and is known for its many applications in higher mathematics. The sum of a function at a point can be described in two different ways: geometrically and physically. Geometrically, the expression of a function at a given value of its input variable is the tangent line to its graph through the given point. It can be found using the slope formula or, if given a graph, by drawing horizontal lines to the input value under investigation. If the graph does not break or jump at that point, then it is simply the y-value corresponding to the given x-value. In Physics, displacement is defined as a physical change. It describes the instantaneous rate of change of an object’s velocity relative to the shortest possible time it takes to travel a given distance. In its relation, the product of a function at a point in a Mathematical view describes the rate of change of the value of the output variables as the values ​​of its corresponding input variables approach zero. In other words, if two carefully chosen values ​​are very close to the given point under question, then the derivative of the function at the point of question is the sum of the difference between the output values ​​and their corresponding input values, since noun is approaching. to zero (0).

In fact, the product of a function is a measure of how a function changes in response to changing values ​​in the input (independent) variable. To find the derivative of a function at a given point, perform the following steps:

1. Select two values, very close to the specified point, one from the left and the other from the right.

2. Solve for the resulting values ​​or y values.

3. Compare the two values.

4. If the two values ​​are equal or will be equal to approximately the same number, then the expression of the function is at that given value of x (the input variable).

5. Using a table of values, if the y-values ​​for those points to the right of the x-value in question are equal to the y-values ​​associated with the y-values ​​of the selected input values ​​to the left of x is close to equal. The value being approximated is the derivative of the function at x.

6. Algebraically, we can first look for the derivative function, taking the limit of the differential equation formula as the denominator approaches zero. Use the derived function to search for the variable using the input variable with the given value of x.

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