What is domain, function and derivative, please explain with simplest examples??
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domain is all the x points along the function or line of points which exist. for example, the domain of y = 2x is all x points because there is nowhere the you can get an answer that doesnt exist. places you do are: if you divide by zero ie: y = 1/x when x=0. another is if you have a negative value under the radical. ie: y = sqrt(x) when x is negative gives you an imaginary number.
this means a domain can be different for each function you look at, but all it is is what points do exist for the function and what points dont.
a function is simply the series of points and how they are defined. it does get more complicated than that in a function can only have one x value for each y value and there is a test for that. but a few examples
y = 2, is a series of points defined by that y is always 2 wherever x is.
y = 2x, a series of points defined by as x changes, y will change.
more complicated functions are still just a variable, y or i can call it f(x), which means a function related to x, defined by x and other numbers like
f(x) = x^2 +4.5x/(x^3+9) and all it is is at different x points there will be some point at (x,f(x)) on a graph
the derivative is more complicated because it represents the slope of an original function. so if you have that original function, we can go to y=2 again. since it is only a straight line, the slope of that function is zero, so if you graph the derivative of y =2, it will by y=0, conventionally we denote the derivative dy/dx, which means the derivative of function why, with taking the derivative of x. say we look at y = 2x. this is a linear slope of 2. the derivative of this is dy/dx = 2 so the graph of this is a straight line at y=2 which was just a straight line at 2 horizontally. and it makes sense because this slope is never changing.