Question:
If $f(x)=x|x|$, then $f^{\prime}(-10)=$ ________.
If $f(x)=x|x|$, then $f^{\prime}(-10)=$ ________.
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The derivative of $x|x|$ is $2|x|$.
Updated On: Jun 26, 2026
- -20
- -10
- -40
- 20
- 40
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Verified By Collegedunia
The Correct Option is D
Solution and Explanation
Step 1: Concept
Define the function based on the sign of $x$.
Step 2: Meaning
For $x < 0$, $|x| = -x$. Thus $f(x) = x(-x) = -x^2$.
Step 3: Analysis
Differentiate: $f'(x) = -2x$ for $x < 0$.
Step 4: Conclusion
$f'(-10) = -2(-10) = 20$. Final Answer: (D)
Define the function based on the sign of $x$.
Step 2: Meaning
For $x < 0$, $|x| = -x$. Thus $f(x) = x(-x) = -x^2$.
Step 3: Analysis
Differentiate: $f'(x) = -2x$ for $x < 0$.
Step 4: Conclusion
$f'(-10) = -2(-10) = 20$. Final Answer: (D)
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