Lesson Example Discussion Quiz: Class Homework |
Step-1 |
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 \$"f"("x") = 3"x"^2 + 2"x" - 5\$. |
|
2 |
Step |
The given function |
\$"f"("x") = 3"x"^2 + 2"x" - 5\$ |
3 |
Step |
To find the derivative of f(x), we apply the power rule by differentiating each term separately |
\$ "d"/"dx" "f"("x") = "d"/"dx"(3"x"^2) + "d"/"dx"(2"x") - "d"/"dx"(5) \$ |
4 |
Formula: |
The power rule formula: |
\$ "d"/"dx" "x"^"n" = "n" "x"^("n" - 1) \$ |
5 |
Formula: |
Constant formula: |
\$ "d"/"dx" "k" = 0 \$ |
6 |
Step |
We can use the power rule to simplify the expression. After applying the rule, we can further simplify the expression |
\$ "f"'("x") = 2(3)"x"^(2 - 1) + 2(1)"x"^(1 - 1) - 0 \$ \$ "f"'("x") = 6"x" + 2 \$ |
7 |
Step |
So, the derivative of f(x) is \$ "f"'("x") = 6"x" + 2 \$. |
|
8 |
Choice.A |
This option represents the correct derivative of the given function \$"f"("x") = 3"x"^2 + 2"x" − 5\$. It correctly applies the power rule to differentiate each term, resulting in 6x for the \$3"x"^2\$ term and 2 for the 2x term |
6x + 2 |
9 |
Choice.B |
This option is incorrect. It seems like it incorrectly multiplies the coefficient of \$"x"^2\$ by 3, resulting in 9x, and the coefficient of x by 1, resulting in 2 |
9x + 2 |
10 |
Choice.C |
This option is incorrect. It represents the derivative of a constant term (-5), which is indeed 0, but it neglects the derivatives of the \$"x"^2\$ and x terms |
0 |
11 |
Choice.D |
This option is incorrect. It represents the antiderivative or integral of the given function rather than its derivative |
\$ "x"^3 + "x"^2 - 5"x" \$ |
12 |
Answer |
Option |
A |
13 |
Sumup |
Can you summarize what you’ve understood in the above steps? |
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