Question:medium
If $f(x)=\frac{|x|}{x^{2}}$ then $f^{\prime}(2)$ is equal to
If $f(x)=\frac{|x|}{x^{2}}$ then $f^{\prime}(2)$ is equal to
Show Hint
Logic Tip: Never attempt to differentiate an absolute value function directly using product/quotient rules without resolving the absolute value first. Since we evaluate at $x=2$ (a positive number), $|x|$ acts exactly like a normal $x$, turning this into a trivial power rule problem.
Updated On: Apr 27, 2026
- $\frac{1}{2}$
- $\frac{1}{4}$
- $-\frac{1}{2}$
- $-\frac{1}{4}$
- $-\frac{1}{6}$
Show Solution
The Correct Option is D
Solution and Explanation
Was this answer helpful?
0
Top Questions on Derivatives
- If \( y = \log_e \left[ e^{3x} \left( \frac{x - 4}{x + 3} \right)^{3/2} \right] \), then find \( \frac{dy}{dx} \):
- MHT CET - 2024
- Mathematics
- Derivatives
- Given \( f'(1) = 3 \), \( f(1) = 1 \), and
\[ y = f\left(f(f(x))\right) + \left(f(x)\right)^2, \] then find \( \frac{dy}{dx} \) at \( x = 1 \).- MHT CET - 2025
- Mathematics
- Derivatives
- If \( y = x^x + x^x \), then find \( \frac{dy}{dx} \):
- MHT CET - 2025
- Mathematics
- Derivatives
- If $ y = \frac{b}{a} $, then $ \frac{dy}{dx} $ is:
- MHT CET - 2025
- Mathematics
- Derivatives
- Want to practice more? Try solving extra ecology questions todayView All Questions
