TS EAMCET · Maths · Differentiation
If \(y=\frac{1}{x}+\cos 2 x\), then \(\frac{d^2 y}{d x^2}\) is equal to
- A \(\frac{2}{x^3}+4 y-\frac{4}{x}\)
- B \(4 y-\frac{4}{x}-\frac{2}{x^3}\)
- C \(\frac{2}{x^3}+\frac{4}{x}-4 y\)
- D \(4 y-\frac{4}{x}-\frac{1}{x^3}\)
Answer & Solution
Correct Answer
(C) \(\frac{2}{x^3}+\frac{4}{x}-4 y\)
Step-by-step Solution
Detailed explanation
\(\begin{aligned} & y=\frac{1}{x}+\cos 2 x \\ & \Rightarrow \quad \frac{d y}{d x}=\frac{-1}{x^2}-2 \sin 2 x \Rightarrow \frac{d^2 y}{d x^2}=\frac{2}{x^3}-4 \cos 2 x \\ & =\frac{2}{x^3}-4\left(y-\frac{1}{x}\right)=\frac{2}{x^3}+\frac{4}{x}-4 y \\ & \end{aligned}\)
See the Complete Solution
Get step-by-step explanations for this and 2.5 Lakh+ more JEE, NEET & CET questions.
- Unlock all solutions
- Practice the full chapter
- Track accuracy across PYQs
4.8 rated on Google Play · 14,000+ reviews
More questions from Maths
- The point on the plane that is nearer to isTS EAMCET 2021 Easy
- The equation of the plane in normal form passing through the point \(A(\bar{a})\), parallel to a vector \(\bar{b}\) and containing a vector \(\bar{c}\) isTS EAMCET 2020 Easy
- \((1, k)\) is a point on the circle passing through the points \((-1,1),(0,-1)\) and \((1,0)\). If \(k \neq 0\), then \(k=\)TS EAMCET 2024 Easy
- The ratio of the maximum and minimum values attained by the function \(f(x)=1+2 \sin x+3 \cos ^2 x, 0 \leq x \leq \frac{2 \pi}{3}\) isTS EAMCET 2020 Easy
- The general solution of the differential equation \(\left(1+y^2\right) d x=\left(\tan ^{-1} y-x\right) d y\) isTS EAMCET 2018 Medium
- The mean of four observations is 3 . If the sum of the squares of these observations is 48 , then their standard deviation isTS EAMCET 2014 Medium
More PYQs from TS EAMCET
- In which of the following reactions, \(t\)-butyl benzene is formed 1. Benzene \(+t\)-butyl chloride \(\stackrel{\mathrm{AlCl}_3}{\longrightarrow}\) 2. Benzene \(+\left(\mathrm{CH}_3\right)_2 \mathrm{C}=\mathrm{CH}_2 \stackrel{\mathrm{BF}_3}{\stackrel{\mathrm{HF}}{\longrightarrow}}\) 3. Benzene \(+t\)-butyl alcohol \(\stackrel{\mathrm{H}_2 \mathrm{SO}_4}{\longrightarrow}\) 4. Benzene + butanoyl chloride \(\underset{\mathrm{Zn} / \mathrm{HCl}}{\stackrel{\mathrm{AlCl}_3}{\longrightarrow}}\)TS EAMCET 2021 Hard
- If the variance of the numbers \(9,15,21, \ldots .,(6 n+3)\) is P, then the variance of the first \(n\) even numbers isTS EAMCET 2025 Hard
- If \(\quad \alpha=\frac{5}{2 ! 3}+\frac{5 \cdot 7}{3 ! 3^2}+\frac{5 \cdot 7 \cdot 9}{4 ! 3^3}+\ldots, \quad\) then \(\alpha^2+4 \alpha\) is equal toTS EAMCET 2008 Medium
- The path of a projectile is given by the equation \(y=a x-b x^2\), where \(a\) and \(b\) are constants and \(x\) and \(y\) are respectively horizontal and vertical distances of projectile from the point of projection. The maximum height attained by the projectile and the angle of projection are respectivelyTS EAMCET 2014 Hard
- The first ionisation energies (in ) of four consecutive elements of the second period are given in the options. The first ionisation energy of nitrogen isTS EAMCET 2021 Hard
- If \(\frac{3+2 i \sin \theta}{1-2 i \sin \theta}\) is a real number and \(0 < \theta < 2 \pi\), then \(\theta\) is equal toTS EAMCET 2002 Easy