TS EAMCET · Maths · Differentiation
If \(y=f(\cosh x)\) and \(f^{\prime}(x)=\log \left(x+\sqrt{x^2-1}\right)\) then \(\frac{d^2 y}{d x^2}=\)
- A \(\sinh x+x \cosh x\)
- B \(x \sinh x\)
- C \(\log \left(x+\sqrt{x^2+1}\right)\)
- D \(\frac{x\left(2 \sqrt{x^2-1}+1\right)}{\sqrt{x^2-1}\left(x^2+\sqrt{x^2-1}\right)}\)
Answer & Solution
Correct Answer
(A) \(\sinh x+x \cosh x\)
Step-by-step Solution
Detailed explanation
\(\frac{d y}{d x} = f^{\prime}(\cosh x) \cdot \sinh x\) \(f^{\prime}(\cosh x) = \log \left(\cosh x+\sqrt{\cosh^2 x-1}\right) = \log \left(\cosh x+\sinh x\right) = \log(e^x) = x\) \(\frac{d y}{d x} = x \sinh x\)…
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