3. Diketahui f(x) Tentakan. 3x-1 dan g(x) = 2x

a) f(x)

b) g'(x)

e) fog' (x)

Given the functions \( f(x) = 3x - 1 \) and \( g(x) = 2x \), let's solve the tasks step by step:

### a) \( f(x) \)
The function \( f(x) \) is already given as:
\[
f(x) = 3x - 1
\]
There is nothing more to calculate here since it's already defined.

### b) \( g'(x) \)
To find \( g'(x) \), we need to differentiate \( g(x) = 2x \) with respect to \( x \). The derivative of \( 2x \) is:
\[
g'(x) = \frac{d}{dx}[2x] = 2
\]

### e) \( (f \circ g)'(x) \) or \( (fog)'(x) \)
This asks for the derivative of the composite function \( f(g(x)) \).

First, find the composition \( f(g(x)) \):
\[
f(g(x)) = f(2x) = 3(2x) - 1 = 6x - 1
\]

Now, differentiate \( f(g(x)) \) with respect to \( x \):
\[
(f \circ g)'(x) = \frac{d}{dx}[6x - 1] = 6
\]

### Summary:
- a) \( f(x) = 3x - 1 \)
- b) \( g'(x) = 2 \)
- e) \( (f \circ g)'(x) = 6 \)

Would you like further clarification on any step?

Here are 5 related questions to extend your understanding:
1. What is the derivative of the function \( h(x) = 3x^2 - 5x + 4 \)?
2. How do you find the derivative of a product of two functions?
3. How would the composition \( (f \circ g)(x) \) change if \( f(x) = x^2 + 1 \)?
4. What is the chain rule and when is it applied?
5. Can you find \( g'(x) \) if \( g(x) = x^3 - 4x^2 + 7x \)?

**Tip**: When differentiating composite functions, always remember to apply the chain rule!

Diketahui f(x) Tentakan. 3x-1 dan g(x) = 2x
a) f(x)
b) g'(x)
e) fog'(x)

Learn how to find derivatives and differentiate composite functions step by step. This example covers differentiation of linear functions and applying the chain rule to composite functions. Suitable for students in Grades 10-12.

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