BASIC DERIVATIVES, DIFFERENTIAL CALCULUS
Most of the time, tackling Calculus gave us a hard start. From the name itself 'Calculi', people use pebbles to calculate. It tells calculations and we don't want that. However, we aren't aware of doing "calculus" in our daily lives. From walking, there are "time rates" already. From lifting the glass of water when we drink there's an application of this subject, when we do balance concerning gravity (knowing that our physical is not perfect geometrical shape), there's the centroid. We do calculus every event of our lives without seeing how its details work.
In every population, its economics was responsible for the status of how it stands. Economists use calculus to read and predict the next outcome. If one community seems to be unprogressed in terms of its economy, it indicates that the tools they're using are weak, and for sure one of those is calculus.
It is by human interest why some proactive paying extra attention to this subject. Scientists use this indispensable tool for accurate predictions such as growth, trajectories, decays, durations, economy, and the like. Those integral complexities of their passions brought us to the comfort of living, There is an existence of calculus behind every physical aspect we enjoy with our senses.
On this page, we will be doing some kind of "baby walk" throughout. Basic Algebraic operations will entertain us like play dough does. Below were the simplest scene, so far, for a good smooth start.
A. This basic formula
B. Illustrations:
Given the equation below, find its first derivative.
We knew that "y" is subject to investigate so as "x". That what the purpose of 'derivation' is. To know the 'what is inside of an object, and its likeness ' , how it works, to function, and so on is the main key to answer our "whys". Given a bread, as we sliced it for eating-defferential calculus applies.Defferential calculus speaks of gradual approaches to zero. In the given equation above, we will apply the formula provided how to derive. Be informed that;
We can use any of those primes and dy/dx.
Now, let's find the first derivative of the given equation above.
C. Examples with Solutions
Find the first derivative the following given equations.
then,
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then,
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, answer , answerD. Problems with Partial Solutions
Find the first derivative of the given equations.
Simple Quiz:
Solve for the first Derivative for each of the given equations. You can write your answer in the comment box. Let see how far did you learn the subject.
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