TS EAMCET · Maths · Differential Equations
If \(x^y=y^x\), then \(x(x-y \log x) \frac{d y}{d x}\) is equal to :
- A \(y(y-x \log y)\)
- B \(y(y+x \log y)\)
- C \(x(x+y \log x)\)
- D \(x(y-x \log y)\)
Answer & Solution
Correct Answer
(A) \(y(y-x \log y)\)
Step-by-step Solution
Detailed explanation
\(\because x^y=y^x\) Taking log on both sides, we get \(y \log x=x \log y\) On differentiating with respect to \(x\), we get \(y \cdot \frac{1}{x}+\log x \frac{d y}{d x}=x \cdot \frac{1}{y} \frac{d y}{d x}+\log y\)…
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
- \(\operatorname{coth}^2 x-\tanh ^2 x=\)TS EAMCET 2025 Medium
- If \(x=\cos ^3 \theta-\sin ^3 \theta\) and \(y=\sqrt[3]{\cos \theta}-\sqrt[3]{\sin \theta}\), then the the value of \(\frac{d y}{d x}\) at \(\theta=\frac{\pi}{4}\) isTS EAMCET 2023 Medium
- If \(\int \frac{\sin ^8 x-\cos ^8 x}{1-2 \sin ^2 x \cos ^2 x} d x=A \sin 2 x+B\), then \(A\) is equal toTS EAMCET 2011 Medium
- If \([t]\) represents the greatest integer \(\leq t\) then the value of \(\lim _{x \rightarrow 3} \frac{11-[2-x]}{[x+10]}\) isTS EAMCET 2025 Medium
- If the lengths of tangents drawn to the circles \(x^2+y^2-8 x+40=0\) \(5 x^2+5 y^2-25 x+80=0\) \(x^2+y^2-8 x+16 y+160=0\) From the point \(P\) are equal, then \(P\) is equal toTS EAMCET 2010 Easy
- \(\left|\begin{array}{ccc}a-b-c & 2 a & 2 a \\ 2 b & b-c-a & 2 b \\ 2 c & 2 c & c-a-b\end{array}\right|\) is equal toTS EAMCET 2008 Easy
More PYQs from TS EAMCET
- Suppose \(\quad f:[-2,2] \rightarrow R \quad\) is defined by \(f(x)=\left\{\begin{array}{ccc}-1, & \text { for } & -2 \leq x \leq 0 \x-1, & \text { for } & 0 \leq x \leq 2 \\{x \in[-2,2]: x \leq 0 & \text { and } & f(|x|)=x\end{array}\right.\) is equal tosTS EAMCET 2003 Medium
- Which of the following statements is/are not correct? (A) Adsorption is accompanied by decrease in enthalpy as well as decrease in entropy of the system. (B) Gases, which can react strongly with adsorbent show chemisorption. (C) When the value of the slope of the Freundlich isotherm is non-zero, adsorption is independent of pressure. (D) Gold number of potato starch is 0.15 .TS EAMCET 2019 Easy
- \(\beta\) is the angle made by the perpendicular drawn from origin to the line \(L \equiv x+y-2=0\) with the positive \(X\)-axis in the anticlockwise direction. If ' \(a\) ' is the \(X\)-intercept of the line \(L=0\) and \(p\) is the perpendicular distance from the origin to the line \(L=0\), then \(a \tan \beta+p^2=\)TS EAMCET 2024 Easy
- The work function of a metal is . Light of frequency falls on this metal. The photoelectric effect will take place only ifTS EAMCET 2021 Easy
- If the slope of a straight line passing through \(\mathrm{A}(3,2)\) is \(3 / 4\), then the coordinates of the two points on the same line that are 5 units away from \(A\) areTS EAMCET 2023 Easy
- \(\lim _{n \rightarrow \infty} \frac{1}{n^2}\left[e^{1 / n}+2 e^{2 / n}+3 e^{3 / n}+\ldots. .+2 n e^2\right]=\)TS EAMCET 2025 Medium