JEE Mains · Maths · STD 12 - 5. continuity and differentiation
If \(\mathrm{y}=\mathrm{y}(\mathrm{x})\) is an implicit function of \(\mathrm{x}\) such that \(\log _{e}(x+y)=4 x y\), then \(\frac{d^{2} y}{d x^{2}}\) at \(x=0\) is equal to .... .
- A \(10\)
- B \(20\)
- C \(30\)
- D \(40\)
Answer & Solution
Correct Answer
(D) \(40\)
Step-by-step Solution
Detailed explanation
\(\ln (x+y)=4 x y \quad(\) At \(x=0, y=1)\) \(x+y=e^{4 x y}\) \(\Rightarrow 1+\frac{d y}{d x}=e^{4 x y}\left(4 x \frac{d y}{d x}+4 y\right)\) At \(x=0 \quad \frac{d y}{d x}=3\)…
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