AP EAMCET · Maths · Differentiation
If \(y=\log (\cosh x)\) then \(\frac{d^2 y}{d x^2}=\)
- A \(\operatorname{sech}^2 x\)
- B \(-\operatorname{sech}^2 x\)
- C \(\sinh x\)
- D \(-\sinh x\)
Answer & Solution
Correct Answer
(A) \(\operatorname{sech}^2 x\)
Step-by-step Solution
Detailed explanation
\(y=\log (\cos \mathrm{h} x)\) Differentiating w.r.t. ' \(x\) ' on both sides \[ \begin{aligned} & \frac{d y}{d x}=\frac{1}{\cosh x}(\sinh x) \\ & \frac{d y}{d x}=\tanh x \end{aligned} \] Again differentiating w.r.t. ' \(x\) ' on both sides…
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