Lesson Example Discussion Quiz: Class Homework |
Step-2 |
Title: Differentiation |
Grade: 1300-a Lesson: S2-L5 |
Explanation: Hello Students, time to practice and review the steps for the problem. |
Lesson Steps
| Step | Type | Explanation | Answer |
|---|---|---|---|
1 |
Problem |
Find the derivative of the function \$"g"("x") = "e"^"x" + "ln"("x")\$. |
|
2 |
Step |
The given function |
\$"g"("x") = "e"^"x" + "ln"("x")\$ |
3 |
Step |
To find the derivative of g(x), we differentiate each term separately using the rules for exponential and logarithmic functions: |
\$ "d"/"dx" "g"("x") = "d"/"dx"("e"^"x") + "d"/"dx"( "ln"("x") ) \$ |
4 |
Formula: |
The differentiation of exponential and logarithmic formulas |
\$ "d"/"dx" "e"^"x" = "e"^"x" \$ \$"d"/"dx"( "ln"("x") ) = 1/"x" \$ |
5 |
Hint |
Now, we can use the above formulas |
\$"g"'("x") = "e"^"x" + 1/"x" \$ |
6 |
Step |
Therefore, the derivative of g(x) is \$"g"'("x") = "e"^"x" + 1/"x" \$. |
|
7 |
Choice.A |
This choice is incorrect because it is inaccurate as it lacks the term \$1/"x"\$ |
\$ "e"^"x" + "x" \$ |
8 |
Choice.B |
This is incorrect because it has extra terms like x and \$"x"^2\$ that are not in the derivative |
\$ "xe"^"x" + "x"^2 \$ |
9 |
Choice.C |
The result obtained is inaccurate due to the absence of the term \$1/"x"\$, rendering it incorrect |
\$ ("e"^"x")/"x" - "x"\$ |
10 |
Choice.D |
This represents the accurate derivative derived from the obtained result |
\$ "e"^"x" + 1/"x"\$ |
11 |
Answer |
Option |
D |
12 |
Sumup |
Can you summarize what you’ve understood in the above steps? |
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