AP EAMCET · Maths · Differentiation
If \(x y \neq 0, x+y \neq 0\) and \(x^m y^n=(x+y)^{m+n}\), where \(m, n \notin N\), then \(\frac{d y}{d x}\) is equal to
- A \(\frac{y}{x}\)
- B \(\frac{x+y}{x y}\)
- C \(x y\)
- D \(\frac{x}{y}\)
Answer & Solution
Correct Answer
(A) \(\frac{y}{x}\)
Step-by-step Solution
Detailed explanation
Given, \(x^m y^n=(x+y)^{m+n}\) On taking log on both sides, we get \(m \log x+n \log y=(m+n) \log (x+y)\) 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
- \(\pi\) is a plane passing through the origin and containing two lines whose direction ratios are \(1,-2,2\) and 2, 3, -1 then direction ratios of the line of intersection of the planes \(x-y-z+1=0\) and \(\pi\) areAP EAMCET 2018 Hard
- Eight different letters of an alphabet are given. Words of four letters from these are formed. The number of such words with at least one letter repeated is :AP EAMCET 2006 Medium
- The distance between the lines represented by \(4 x^2+20 x y+25 y^2+2 x+5 y-12=0\) is equal toAP EAMCET 2022 Medium
- \(\lim _{n \rightarrow x} \sqrt{2}\left[\frac{(2+\sqrt{2})^n+(2-\sqrt{2})^n}{(2+\sqrt{2})-(2-\sqrt{2})^n}\right]=\)AP EAMCET 2022 Medium
- A team of 5 students is to be selected from 12 students. If two particular students are to be included in that team, then the number of ways that such team can be selected isAP EAMCET 2023 Medium
- The number of natural numbers less than 1000 , in which no two digits are repeated, is :AP EAMCET 2006 Medium
More PYQs from AP EAMCET
- If \(\quad \cos 2 x=(\sqrt{2}+1)\left(\cos x-\frac{1}{\sqrt{2}}\right), \cos x \neq \frac{1}{2}\), then \(x \in\)AP EAMCET 2005 Hard
- The tangents drawn to the hyperbola \(5 \mathrm{x}^2-9 \mathrm{y}^2=90\) through a variable point P make the angles \(\alpha\) and \(\beta\) with its transverse axis. If \(\alpha, \beta\) are the complementary angles, then the locus of P isAP EAMCET 2025 Medium
- The angle subtended by the normal chord at the point \((9,9)\) on the parabola \(y^2=9 x\), at the focus of the parabola isAP EAMCET 2017 Hard
- In \(\triangle A B C\), if \(\mathrm{A}\) is \((1,2), \mathrm{B}\) and \(\mathrm{C}\) lie on \(\mathrm{y}=\mathrm{x}+\alpha\) (where \(\alpha\) is variable), then the locus of the orthocenter of the triangle isAP EAMCET 2022 Medium
- \(\cos ^3 110^{\circ}+\cos ^3 10^{\circ}+\cos ^3 130^{\circ}=\)AP EAMCET 2018 Easy
- In the random experiment of tossing two unbiased dice let \(E\) be the event of getting the sum 8 and \(F\) be the event of getting even numbers on both the dice. Then :
I. \(P(E)=\frac{7}{36}\)
II. \(P(F)=\frac{1}{3}\)
Which of the following is a correct statement?AP EAMCET 2006 Hard