AP EAMCET · Maths · Differentiation
\(y=e^{a \sin ^{-1} x} \Rightarrow\left(1-x^2\right) y_{n+2}-(2 n+1) x y_{n+1}\) is equal to
- A \(-\left(n^2+a^2\right) y_n\)
- B \(\left(n^2-a^2\right) y_n\)
- C \(\left(n^2+a^2\right) y_n\)
- D \(-\left(n^2-a^2\right) y_n\)
Answer & Solution
Correct Answer
(C) \(\left(n^2+a^2\right) y_n\)
Step-by-step Solution
Detailed explanation
Given, \(\quad y=e^{a \sin ^{-1} x}\) On differentiating w.r.t. \(x\), we get \(\begin{aligned} & y_1=e^{a \sin ^{-1} x} a \cdot \frac{1}{\sqrt{1-x^2}} \\ \Rightarrow \quad & y_1 \sqrt{1-x^2}=a y \\ \Rightarrow \quad & \left(1-x^2\right) y_1^2=a^2 y^2 \end{aligned}\) Again,…
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
- A random variable X follows a binomial distribution in which the difference between its mean and variance is 1. If \(2 \mathrm{P}(\mathrm{x}=2)=3 \mathrm{P}(\mathrm{x}=1)\), then \(\mathrm{n}^2 \mathrm{P}(\mathrm{x}>1)=\)AP EAMCET 2025 Medium
- The figure formed by the four points \((\hat{\mathbf{i}}+\hat{\mathbf{j}}-\hat{\mathbf{k}}),(2 \hat{\mathbf{i}}+3 \hat{\mathbf{j}}),(5 \hat{\mathbf{j}}-2 \hat{\mathbf{k}})\) and \((\hat{\mathbf{k}}-\hat{\mathbf{j}})\) isAP EAMCET 2021 Easy
- If [.] here denotes the greatest integer function, \(\lim _{x \rightarrow 0} x^7\left[\frac{1}{x^3}\right]\) is equal toAP EAMCET 2021 Medium
- The equation of a circle touching the coordinate axes and the line \(3 x-4 y=12\) isAP EAMCET 2018 Easy
- The solution of \(\tan y \frac{d y}{d x}=\sin (x+y)+\sin (x-y)\) isAP EAMCET 2010 Hard
- If \(I\) is the identity matrix of order 2 and \(A=\left[\begin{array}{ll}1 & 1 \\ 0 & 1\end{array}\right]\), then for \(n \geq 1\), mathematical induction givesAP EAMCET 2013 Medium
More PYQs from AP EAMCET
- The ratio of the strengths of the four fundamental forces in nature, \(\mathrm{F}_{\mathrm{G}}: \mathrm{F}_{\mathrm{N}}: \mathrm{F}_{\mathrm{E}}: \mathrm{F}_{\mathrm{W}}=\)AP EAMCET 2020 Easy
- If \(3 x+y+k=0\) is a tangent to the circle \(x^2+y^2=10\), then \(k=\ldots . . .\).AP EAMCET 2020 Easy
- What is the indicator used in Argentometric titrations?AP EAMCET 2025 Easy
- Consider the two following statements \(A\) and \(B\), and identify the correct choice given in the answers : \((A)\) Duddell's thermo galvanometer is suitable to measure direct current only. (B) Thermopile can measure temperature differences of the order of \(10^{-3}{ }^{\circ} \mathrm{C}\).AP EAMCET 2003 Medium
- If the longest wavelength of spectral line of Paschen series of \(\mathrm{Li}^{2+}\) ion spectrum is \(x Å\), then the longest wavelength (in \(Å\) ) of Lyman series of hydrogen spectrum isAP EAMCET 2024 Medium
- Eight spherical rain drops of the same mass and radius are falling down with a terminal speed of \(6 \mathrm{~cm}-\mathrm{s}^{-1}\). If they coalesce to form one big drop, what will be the terminal speed of bigger drop? (Neglect the buoyancy of the air)AP EAMCET 2009 Easy