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.?

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3 Answers
Aug 16, 2017

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

Aug 16, 2017

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.

Aug 16, 2017

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