COMEDK · Maths · 26. Differentiation
If \(y=\sqrt{\dfrac{x}{a}}+\sqrt{\dfrac{a}{x}}, \quad\) then \(2 x y \dfrac{d y}{d x}\) is equal to
- A \(x+\dfrac{a}{x}\)
- B \(\dfrac{a}{x}-\dfrac{x}{a}\)
- C \(\dfrac{x^2+a^2}{a x}\)
- D \(\dfrac{x}{a}-\dfrac{a}{x}\)
Answer & Solution
Correct Answer
(D) \(\dfrac{x}{a}-\dfrac{a}{x}\)
Step-by-step Solution
Detailed explanation
Given \(y = \sqrt{\dfrac{x}{a}} + \sqrt{\dfrac{a}{x}} = \dfrac{\sqrt{x}}{\sqrt{a}} + \dfrac{\sqrt{a}}{\sqrt{x}}\). Differentiating with respect to \(x\): \(\dfrac{dy}{dx} = \dfrac{1}{\sqrt{a}} \cdot \dfrac{1}{2\sqrt{x}} + \sqrt{a} \cdot \left( -\dfrac{1}{2} x^{-3/2} \right)\)…
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 circle \(x^{2}+y^{2}-8 x+4 y+4=0\) touchesCOMEDK 2013 Easy
- The value of \(\left|\begin{array}{ccc}x+y & y+z & z+x \\ x & y & z \\ x-y & y-z & z-x\end{array}\right|=\)COMEDK 2016 Medium
- \(\text { If } a \mathcal{N}=\{a x: x \in \mathcal{N}\} \text {, then } 3 \mathcal{N} \cap 7 \mathcal{N} \text { is }\)COMEDK 2024 Easy
- \(\int_0^2\left|x^2+2 x-3\right| d x \text { is equal to }\)COMEDK 2023 Medium
- The characteristic roots of the matrix \(\left[\begin{array}{ccc}1 & 0 & 0 \\ 2 & 3 & 0 \\ 4 & 5 & 6\end{array}\right]\) areCOMEDK 2019 Easy
- \(\text { The general solution of the differential equation } \dfrac{d y}{d x}=\dfrac{x y}{x^2+y^2} \text { is }\)COMEDK 2024 Medium
More PYQs from COMEDK
- A wire of length \(2 \mathrm{~m}\) is made from \(10 \mathrm{~cm}^{3}\) of copper. A force \(F\) is applied so that its length increases by \(2 \mathrm{~mm}\). Another wire of length \(8 \mathrm{~m}\) is made from the same volume of copper. If the force \(F\) is applied to it, its length will increase byCOMEDK 2014 Medium
- The Enthalpy of combustion of 1.0 mole of a reactive metal X at \(27^{\circ} \mathrm{C}\) and 1.0 bar pressure to form a solid oxide (XO) is \(-601.83 \mathrm{~kJ} / \mathrm{mol}\). The Internal energy change for this reaction is ______ kJ .
\(\left(\mathrm{R}=8.314 \mathrm{j} \mathrm{~K}^{-1} \mathrm{~mol}^{-1}\right)\)COMEDK 2025 Medium - The general solution of \(\frac{d y}{d x}=1+x+y+x y\), \(y=\)COMEDK 2024 Medium
- The coefficient of \(x^{24}\) in the expansion of \(\left(1-x^5\right)^{10}\) isCOMEDK 2024 Easy
- The number of antibonding electron pairs in \(\mathrm{O}_{2}^{2-}\) molecular ion on the basis of molecular orbital theory is
[Atomic number of \(\mathrm{O}\) is 18 ]COMEDK 2020 Medium - \(\int \dfrac{2 x}{\sqrt{1-x^2-x^4}} d x=\sin ^{-1}[f(x)]+c\) then \(f(x)=\)COMEDK 2025 Medium