AP EAMCET · Maths · Differentiation
If \(y=f(x)\) is twice differentiable function such that at a point \(P, \frac{d y}{d x}=4, \frac{d^2 y}{d x^2}=-3\), then \(\left(\frac{d^2 x}{d y^2}\right)_P=\)
- A \(\frac{64}{3}\)
- B \(\frac{16}{3}\)
- C \(\frac{3}{16}\)
- D \(\frac{3}{64}\)
Answer & Solution
Correct Answer
(D) \(\frac{3}{64}\)
Step-by-step Solution
Detailed explanation
\begin{array}{ll} \because \frac{d^2 x}{d y^2} =\frac{d}{d y}\left(\frac{d x}{d y}\right)=\frac{d x}{d y} \frac{d}{d x}\left(\frac{1}{\left(\frac{d y}{d x}\right)}\right) \\ =\left(\frac{d x}{d y}\right)\left(\frac{-\frac{d^2 y}{d x^2}}{\left(\frac{d y}{d…
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