AP EAMCET · Maths · Differentiation
If \(x^2+y^2+\sin y=4\), then the value of \(\frac{d^2 y}{d x^2}\) at \(x=-2\) is
- A \(-30\)
- B \(-34\)
- C \(-32\)
- D \(-18\)
Answer & Solution
Correct Answer
(B) \(-34\)
Step-by-step Solution
Detailed explanation
\( (-2)^2+y^2+\sin y=4 \) \( 4+y^2+\sin y=4 \) \( y^2+\sin y=0 \Rightarrow y=0 \) \( 2x+2y\frac{dy}{dx}+\cos y\frac{dy}{dx}=0 \) \( \frac{dy}{dx}=\frac{-2x}{2y+\cos y} \) \( \frac{dy}{dx} \Big|_{(-2,0)} = \frac{-2(-2)}{2(0)+\cos(0)} = \frac{4}{1} = 4 \)…
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