TS EAMCET · Maths · Differentiation
If \(\quad z=\sec ^{-1}\left(\frac{x^4+y^4-8 x^2 y^2}{x^2+y^2}\right), \quad\) then \(x \frac{\partial z}{\partial x}+y \frac{\partial z}{\partial y}\) is equal to
- A \(\cot z\)
- B \(2 \cot z\)
- C \(2 \tan z\)
- D \(2 \sec z\)
Answer & Solution
Correct Answer
(B) \(2 \cot z\)
Step-by-step Solution
Detailed explanation
Given that, \[ \begin{aligned} z & =\sec ^{-1}\left(\frac{x^4+y^4-8 x^2 y^2}{x^2+y^2}\right) \\ \Rightarrow \quad \sec z & =\frac{x^4+y^4-8 x^2 y^2}{x^2+y^2} \end{aligned} \] Here, \(\quad n=2\)…
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 coefficient of \(x^{24}\) in the expansion of \(\left(1+x^2\right)^{12}\left(1+x^{12}\right)\left(1+x^{24}\right)\) isTS EAMCET 2009 Easy
- The line \(2 x+y=1\) is a tangent to the hyperbola \(\frac{x^2}{a^2}-\frac{y^2}{b^2}=1(a>b)\). If this line passes through the point of intersection of a directrix and the positive \(X\)-axis, then the eccentricity of that hyperbola isTS EAMCET 2019 Medium
- \(a\) and \(b\) are the semi-major and semi-minor axes of an ellipse whose axes are along the coordinate axes. If its latus rectum is of length 4 units and the distance between its foci is \(4 \sqrt{2}\), then \(a^2+b^2=\)TS EAMCET 2024 Easy
- If \(\mathrm{A}(1,2,3), \mathrm{B}(3,7,-2), \mathrm{C}(6,7,7)\) and \(\mathrm{D}(-1,0,-1)\) are points in a plane, then the vector equation of the line passing through the centroids of \(\triangle \mathrm{ABD}\) and \(\triangle \mathrm{ACD}\) isTS EAMCET 2023 Easy
- Two friends \(A\) and \(B\) meet every weekend either at a party or at a Sports Club. The probability that they meet at Sports Club is \(\frac{4}{9}\). The probability that they will dine together at a party and at the Club are respectively \(\frac{1}{3}\) and \(\frac{2}{5}\). On a certain weekend the probability that they disperse without dine together isTS EAMCET 2021 Easy
- If \(\overrightarrow{\mathbf{a}}=\hat{\mathbf{i}}+\hat{\mathbf{j}}+\hat{\mathbf{k}}, \overrightarrow{\mathbf{b}}=\hat{\mathbf{i}}-\hat{\mathbf{j}}+\hat{\mathbf{k}}, \quad \overrightarrow{\mathbf{c}}=\hat{\mathbf{i}}+\hat{\mathbf{j}}-\hat{\mathbf{k}}\) and \(\overrightarrow{\mathbf{d}}=\hat{\mathbf{i}}-\hat{\mathbf{j}}-\hat{\mathbf{k}}\), then observe the
following The correct match of List-I to List-II \(\begin{array}{llll}\text { i } & \text { ii } & \text { iii } & \text { iv }\end{array}\)TS EAMCET 2008 Easy
More PYQs from TS EAMCET
- For any integer \(n \geq 2\), let \(I_n=\int \tan ^n x d x\). If \(I_n=\frac{1}{a} \tan ^{n-1} x-b I_{n-2}\) for \(n \geq 2\), then the ordered pair \((a, b)\) equals toTS EAMCET 2014 Hard
- The refractive index of the material of a small angled prism is 1.6 . If the angle of minimum deviation is \(4.2^{\circ}\), the angle of the prism isTS EAMCET 2024 Easy
- Which of the following is not a fundamental force in nature?TS EAMCET 2021 Easy
- If \(f(x)=\sin x+\cos x\), then \(f\left(\frac{\pi}{4}\right) f^{(i v)}\left(\frac{\pi}{4}\right)\) is equal toTS EAMCET 2010 Easy
- If where thenTS EAMCET 2021 Easy
- A circular copper ring at \(30^{\circ} \mathrm{C}\) has a hole with an area of \(9.98 \mathrm{~cm}^2\). It is made to slip onto a steel rod of crosssectional area of \(10 \mathrm{~cm}^2\), by raising the temperature of both ring and rod simultaneously by an amount \(\Delta \mathrm{T}\). If the coefficient of linear expansion of copper and steel are \(17 \times 10^{-6} /{ }^{\circ} \mathrm{C}\) and \(11 \times 10^{-6} /{ }^{\circ} \mathrm{C}\), then minimum value of \(\Delta \mathrm{T}\) should beTS EAMCET 2022 Hard