COMEDK · Maths · 26. Differentiation
\(\text { If } y=\sin ^{-1}\left(\dfrac{5 x+12 \sqrt{1-x^2}}{13}\right) \text { then } \dfrac{d y}{d x} \text { equals }\)
- A \(\dfrac{-1}{\sqrt{1+x^2}}\)
- B \(\dfrac{-2 x}{\sqrt{1-x^2}}\)
- C \(\dfrac{1}{\sqrt{1-x^2}}\)
- D \(\dfrac{2 x}{\sqrt{1-x^2}}\)
Answer & Solution
Correct Answer
(C) \(\dfrac{1}{\sqrt{1-x^2}}\)
Step-by-step Solution
Detailed explanation
Given \(y = \sin^{-1} \left( \dfrac{5x + 12\sqrt{1-x^2}}{13} \right)\). Let \(x = \sin \theta\), where \(\theta = \sin^{-1} x\). Then \(\sqrt{1-x^2} = \cos \theta\). Substituting these into the expression for \(y\):…
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