JEE Mains · Maths · STD 12 - 5. continuity and differentiation
If \(y(x)=x^2, x > 0\), then \(y^{\prime \prime}(2)-2 y^{\prime}(2)\) is equal to :
- A \(8 \log _e 2-2\)
- B \(4 \log _e 2+2\)
- C \(4\left(\log _e 2\right)^2-2\)
- D \(4\left(\log _e 2\right)^2+2\)
Answer & Solution
Correct Answer
(C) \(4\left(\log _e 2\right)^2-2\)
Step-by-step Solution
Detailed explanation
\(y^{\prime}=x^x\) \(y^{\prime}=x^x(1+\ell n x)\) \(y^{\prime \prime}=x^x(1+\ell nx )^2+x^x \cdot \frac{1}{x}\) \(y^{\prime \prime}(2)=4(1+\ell n 2)^2+2\) \(y^{\prime}(2)=4(1+\ell n 2)\) \(y^{\prime \prime}(2)-2 y ^{\prime}(2)=4(1+\ell n 2)^2+2-8(1+\ell n 2)\)…
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