Question

Solve 22 and 24 number.it is simple differentiation but tell me what is mean by f(x) and g(x) here and how solve it.i am very worried.?

Answer 1

See explanation.

Explanation:

Questions 22 and 24 are the basic properties of derivatives.

22 says that the derivative of a difference of 2 functions is the difference of the functions' derivatives

24 says that the derivative of a sum of 3 functions is the sum of the functions' derivatives.

In these questions `f(x)`, `g(x)` and `h(x)` are any functions whose derivative is defined

Answer 2

Please see below.

Explanation:

I think that you are asking about the notation `f(x)`.

We use this notation for a function.

One way to think about a function is simply as another name for `y`.

So instead of writing

`y = x^2+3`

We can write

`f(x) = x^2+3`
We read this "f of x equals x squared plus 3".
`f` is the name of the function and `f(x)` is a name for `y`.

Instead of writing:

If `y = x^2+3`, find `y` when `x = 2`

We can write

If `f(x) = x^2+3`, find `f(3)`
We read `f(3)` as "f of 3`and, since`(3)^2+3 = 9#, we say "f of 3 is [or equals] 9".

A function is like an operation performed on some input. It takes an input and gives an output. Some of the algebra operations and some calculator buttons are (simple) functions.

With `y = f(x)` we write `f'(x)` (read "f prime of x") for `dy/dx`

Instead of saying

Find `dy/dx` when `x = 5`

we can say

Find `f'(5)` ("find f prime of 5")

You can read more about functions at Socratic under the Subject: Algebra.
Use the Subject pull-down list above. Select Algebra.
Then when Algebra loads, select Topics. You can look for topics about functions.

On a personal note

Many students are now taught about functions when they learn algebra. The first time I saw a function or the word "function" was in my first calculus class.
For a long time I thought of functions as I have described them. `f(x) is another name for`y#.
There's more to it than that, but it gets you going in the right direction.

Answer 3

Question 22 could be rewritten as follows.

With `y = f(x)` and `z = g(x)`

what is `d/dx(y-z)`?

Answer (C.) `f'(x)-g'(x)` is the same as `dy/dx-(dz)/dx`