AP EAMCET · Maths · Differentiation
If \(y=\frac{\sin \mathrm{h}^{-1} x}{\sqrt{1+x^2}}\), then \(\left(1+x^2\right) \mathrm{y}_2+3 \mathrm{xy}_1+\mathrm{y}=\)
- A 2
- B 1
- C -1
- D 0
Answer & Solution
Correct Answer
(D) 0
Step-by-step Solution
Detailed explanation
\[ \begin{aligned} & \text { Given, } y=\frac{\sinh ^{-1} x}{\sqrt{1+x^2}} \\ & \sqrt{1+x^2} y=\sinh ^{-1} x \end{aligned} \] On differentiating w.r.t. \(x\), we get…
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
- If the axes are translated to the orthocentre of the triangle formed by the points \(\mathrm{A}(7,5), \mathrm{B}(-5,-7), \mathrm{C}(7,-7)\), then the coordinates of the incentre of the triangle in the new system areAP EAMCET 2025 Hard
- AP EAMCET 2022 Hard
- If \(A+B=\frac{\pi}{4}\), then \(\frac{\cos B-\sin B}{\cos B+\sin B}=\)AP EAMCET 2025 Medium
- If \(\mathrm{a}, \mathrm{b}\) and \(\mathrm{c}\) are non-zero vectors such that \(\mathrm{a}\) and \(\mathrm{b}\) are not perpendicular to each other, then the vector \(\mathbf{r}\) which is perpendicular to \(\mathbf{a}\) and satisfying \(\mathrm{r} \times \mathrm{b}=\mathrm{c} \times \mathrm{b}\) isAP EAMCET 2017 Medium
- The equations of the latusrectum of the ellipse \(9 x^2+4 y^2-18 x-8 y-23=0\) areAP EAMCET 2018 Medium
- If \(\sin (x+3 \alpha)+3 \sin (x-\alpha)=0\), thenAP EAMCET 2017 Easy
More PYQs from AP EAMCET
- The current gain for a transistor working as common base amplifier is 0.96 . If the emitter current is \(7.2 \mathrm{~mA}\), then the base current isAP EAMCET 2021 Medium
- The work done by 6 moles of helium gas when its temperature increases by \(20^{\circ} \mathrm{C}\) at constant pressure is
(Universal gas constant \(=8.31 \mathrm{~J} \mathrm{~mol}^{-1} \mathrm{~K}^{-1}\) )AP EAMCET 2025 Medium - Observe the following data.
\(\mathrm{Q}^{\mathrm{a}+}, \mathrm{X}^{\mathrm{b}+}, \mathrm{Y}^{\mathrm{c}+}, \mathrm{Z}^{\mathrm{d}+}\) are respectivelyIon \(\mathrm{Q}^{\mathrm{a}+}\) \(\mathrm{X}^{\mathrm{b}+}\) \(\mathrm{Y}^{\mathrm{c}+}\) \(\mathrm{Z}^{\mathrm{d}+}\) Radius (pm) \(53\) \(66\) \(40\) \(100\) AP EAMCET 2025 Medium - If \(\frac{6 x^3+7 x^2+6 x-3}{(x-1)(x+3)\left(x^2+1\right)}=\frac{A}{x-1}+\frac{B}{x+3}+\frac{C x+D}{x^2+1}\)
and \(n=A+B+C+D\) and \({ }^{50} C_n={ }^{50} C_r\), then \(r\) is equal toAP EAMCET 2021 Medium - In a \(\triangle A B C\), if \(b=2, c=3\) and \(\angle B=\frac{\pi}{6}\), then \(a\) satisfies the equationAP EAMCET 2021 Easy
- An electrical refrigerator with \(\beta=5\) extracts \(5000 \mathrm{~J}\) from the contents of the refrigerator. During this process, find the electrical energy utilised by its motor.AP EAMCET 2020 Medium