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Shortcut used: Identify the required derivative rule, differentiate symbolically, and verify signs and evaluation points.
Solve in 3 steps:
- Mark the given values and the exact target.
- Apply the relevant formula, rule, or concept.
- Check the final value against the options.
Common mistake: Do not choose an option before confirming the exact demand of the question.
Question 2
Multiple Choice Question
Question
If f(x)=x^2 e^x, what is f'(x)?
Explanation
Correct Answer: B
ANSWER
Correct Answer: B
Method / Topic: Derivatives
The product rule gives 2xe^x+x^2e^x=e^x(x^2+2x).
Why this answer is correct
The correct option matches the required rule and the given information.
Short Explanation
The product rule gives 2xe^x+x^2e^x=e^x(x^2+2x).
Detailed Explanation
Question
If f(x)=x^2 e^x, what is f'(x)?
ANSWER
Correct Answer: B
Method / Topic: Derivatives
The product rule gives 2xe^x+x^2e^x=e^x(x^2+2x).
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Question 2
Learn + Solve: Shortcut, Trap & Fast Route Click to view shortcut, steps, and common mistake
Learn + solve
Shortcut used, common trap, and the fastest solving route
Shortcut used: Identify the required derivative rule, differentiate symbolically, and verify signs and evaluation points.
Solve in 3 steps:
- Mark the given values and the exact target.
- Apply the relevant formula, rule, or concept.
- Check the final value against the options.
Common mistake: Do not choose an option before confirming the exact demand of the question.
Question
If f(x)=x^2 e^x, what is f'(x)?
Explanation
Correct Answer: B
ANSWER
Correct Answer: B
Method / Topic: Derivatives
The product rule gives 2xe^x+x^2e^x=e^x(x^2+2x).
Why this answer is correct
The correct option matches the required rule and the given information.
Short Explanation
The product rule gives 2xe^x+x^2e^x=e^x(x^2+2x).
Detailed Explanation
Question
If f(x)=x^2 e^x, what is f'(x)?
ANSWER
Correct Answer: B
Method / Topic: Derivatives
The product rule gives 2xe^x+x^2e^x=e^x(x^2+2x).
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Concept tagged
Identify the required derivative rule
differentiate symbolically
and verify signs and evaluation points.