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Math for Students: How to Solve Derivatives

Solving various equations in mathematics is one of the main requirements for students of technical universities. The conditions differ depending on the specialty, but the general rules remain the same.

The complexity of the equation may differ, but the principle of the solution remains. Derivative is one of the basic concepts of calculus. Knowledge of this concept and calculation methods allows solving problems in physics and mathematics, as well as related sciences, such as economics. And we at really want you to understand this issue as well as we do.  

Physical and geometric meaning

The solution to a derivative starts with understanding it. First of all, it is necessary to understand what its geometric and physical meaning is. This will help you learn how to calculate it and understand it. Mathematics is not as difficult as a subject, when the study allows you to gradually climb the steps from simple to complex. This is a way to disassemble everything step by step and not leave unresolved questions.   

In order to determine the physical and geometric meaning, you need to turn to the functions for help. As an example, we can take a certain f (x), which is specified in the interval (a, b). In this case, the points x0 and x are part of this interval. If a condition is met that changes x when there is a change in the function itself as a whole. Any changes to the argument are the difference between the x-x0 value. The described process is usually called an increment for an argument and is called delta x. Any increment or change is usually called a difference in values.

The derivative at one point is the limit of its increment to the incremented argument, as it tends to 0. Hence the meaning, in physical and geometric terms, respectively:

  • The derivative of the path according to the time interval is equal to the speed of movement in a straight line;
  • The derivative at a point is equal to the tangent of the angle formed in the interval from the given point to the OX axis.

This is a variation of the method for resolving questions in physics regarding the speed and time of movement of an object. How is the concept of speed explained? This is the quotient of the path x = f (t) and the time t. According to this understanding, it is possible to find out the speed that an object developed over a certain period of time. For this purpose, the limit is calculated for the time instant t0. The solution allows you to determine the speed at the exact moment in time, which is important in the process of performing various equations in physics. Hence the practical meaning of such calculations emerges. It also happens that while writing a dissertation, one has to use this mathematical method of analysis and the student is mistaken with such an easy task, because his brain is corny overloaded with more complicated things. But we at essay assistant will always be happy to check your work for errors in your dissertation in mathematics


The search process is usually called differentiation. The need to define functions of varying degrees of complexity has led to the emergence of clear rules. This created a table of derivatives and simplified the calculation process. A set of clear rules and outcomes helped to simplify the entire process. The first scientists who began to clarify this concept were G.V. Leibniz and I. Newton.

When performing these steps for any function, it is not necessary to engage in self-determination of the solution. It is much easier to use a ready-made table with results. There is no need to invent something new and waste a lot of time, you just need to navigate according to clear rules. This will allow you to quickly calculate the limit of the ratio of the increments. The ready-made algorithm simplifies the question even more:

  • The expression that is under the stroke sign must be divided into separate simple parts;
  • Determine how they are related (quotient, sum or product);
  • Table solution for elementary concepts;
  • Selection of formulas, and taking into account the rules of differentiation.

It is always necessary to take into account the laws of differentiation and the table to make it easier for yourself. An extremely simple algorithm will allow you to solve even the most difficult problem. The most important principle that must be observed is to always follow from simple concepts to complex ones. If a difficult task is immediately set, you need to divide it into elementary parts and solve it according to the above principle. Differentiation is something other than a computation process.

Search and find rules

A function with a derivative at a specific given point is differentiable. Hence the very name of the process arises. It takes a long time to make an independent decision. It all starts with drawing up the ratio of the argument increment and f (x). Next, you need to calculate the limit that tends to 0 of the argument increment. The complex process is effective, but it takes a lot of effort. To do this, it is better to use the table for elementary concepts and take into account the calculation rules. So you can find out the answer for the most difficult problems. A set of clear rules will help you with this:

  1. Removal of a constant is carried out outside its signs. Simplification of the expression is performed whenever possible.
  2. Determination of the amount - is the sum of the derivatives. The rule is also relevant for the difference of the same name.
  3. Calculation of the derivative of the product - is calculated according to: (uv)? = u? v + uv ?. For complex variations, the equation is made with an intermediate argument in mind. It is first evaluated for the outer f (x) by an intermediate argument. Next, you need to multiply by the result of the intermediate argument for the independent variable. 
  4. Definition of the concept for private 2 functions by the formula.

Examples with solutions can help simplify the computation problem, but not always. Often in the examples you can find peculiar traps that are misleading and prevent you from solving something. Carefulness and adherence to the rules will help in determining the correct result. And if it so happens that you had to deal with these tasks, because Thurs of you learn from related field, such as economic when training an accountant and you are too difficult to solve these things, you can always ask for help from professionals

We are always glad to know that students have received a new dose of knowledge and figured out something difficult. We are happy to help them with this!



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