AP EAMCET · Maths · Differentiation
If \(x=f(\theta)\) and \(y=g(\theta)\), then \(\frac{d^2 y}{d x^2}=\)
- A \(\frac{g^{\prime \prime}(\theta)}{f^{\prime}(\theta)}\)
- B \(\frac{f^{\prime \prime}(\theta)}{x(\theta)}\)
- C \(\frac{f^{\prime}(\theta) g^{\prime \prime}(\theta)-g^{\prime}(\theta) f^{\prime \prime}(\theta)}{\left(f^{\prime}(\theta)\right)^3}\)
- D \(\frac{g^{\prime}(\theta) f^{\prime \prime}(\theta)-g^{\prime \prime}(\theta) f^{\prime \prime}(\theta)}{\left(g^{\prime \prime}(\theta)\right)^3}\)
Answer & Solution
Correct Answer
(C) \(\frac{f^{\prime}(\theta) g^{\prime \prime}(\theta)-g^{\prime}(\theta) f^{\prime \prime}(\theta)}{\left(f^{\prime}(\theta)\right)^3}\)
Step-by-step Solution
Detailed explanation
Given, \(x=f(\theta)\) and \(y=g(\theta)\) \(\frac{d x}{d \theta}=f^{\prime}(\theta), \frac{d y}{d \theta}=g^{\prime}(\theta)\) \(\Rightarrow \quad \frac{d y}{d x}=\frac{g^{\prime}(\theta)}{f^{\prime}(\theta)}\)…
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