I have some basic questions from calculus

Can someone please clear that for me ?

I am not good at mathematics , before i even attempt to learn calculus properly .

I need to get some clarity about a few basic things .





What exactly is a function ?

for example ,

y=5x+6

In that equation ,

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Most times you see an equation, the dependent variable will be isolated on one side. The independent variable is usually designated by x. The dependent variable is typically designated by y. However, any variables could be used in place of x or y. In the equation below the dependent variable is y

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Independent variables (inputs) are fed into your machine (i.e. your formula) to see what the output is (i.e. what the values of your dependent variables are)

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Is calculus about the relationship between the two different unknown's in an y x graph ?

I will narrow down my question one more time .

What exactly is a derivative of a function ?

I also know it as instant rate of change .

Is derivative the relationship between the two different unknown's in an y x graph ?

Ok, I'm not a mathematician but...

A derivative gives you the rate of change of a function at a particular point.
In your example y=5x + 6 we can say that y is a function of X, I e. that you will get a different value of y for each different value of X.
The derivative of y with respect to X (written as dy/dx) gives you the rate of change of y when X is changed. If you plotted a graph this would be equal to the gradient. In your example dy/dx = 5. If you plotted a graph if y Vs X you would get a straight line with a gradient of 5 meeting the y axis at y=6.

Thank you for the reply PhDemon ,

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The slope of a line is a measure of how fast it is changing. This can be for a straight line -- where the slope tells you exactly how far up (positive slope) or down (negative slope) a line goes while it goes how far across. Slope can also be used for a line tangent to a curve. Or, it can be for a curved line when doing Calculus, where slope is also known as the "derivative" of a function. Either way, think of slope simply as the "rate of change" of a graph: if you make the variable "x" bigger, at what rate does "y" change? That is a way to see slope as a cause and an effect event

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I also learned about the importance of a point , its co ordinates

The importance of secant lines

And how difference quotient is derived from it

Not a bad day :)

I am mathematician.
some responses to your (basic) questions.

1. a function (f) is an operation from A set to a B set , such that;

i. there should be no element in A which is not paired with any element in B (all elements of A set should be paired with an element in B)
ii. Any element of A set should be paired with no more than one element in B.

2. any function is defined with at least one dependent and independent variable.

3) 5x + 6 is in the form of ax +b wherein a and b are real numbers ,which is linear function.

4) derivativeness is a definition for functions defined by one variable. when there are two or several variables or more, then the definition changes to differentiation. (you may check differentiable functions)

simply derivativeness is that the limit of rate of operated values (i.e. in B above) to normal values (i.e. in A).

reference: any analysis book for science and / or engineering (prefereably for engineering because your question smells engineering.)

@unknown_artist

Thanks for the explanation .




I simply wrote this down to refresh my mathematics

Algebra , Find the unknown x
Differentiation , Find the unknown instantaneous rate of change
Integration , Find the unknown area underneath an instantaneous rate of change
Differential equation , Find the unknown function


I hope its not that wrong