COMEDK · Maths · 26. Differentiation
\(\text { If } y=f(x), \quad p=\dfrac{d y}{d x} ; q=\dfrac{d^2 y}{d x^2} \text { then } \dfrac{d^2 x}{d y^2} \text { is equal to }\)
- A \(\dfrac{q}{p^2}\)
- B \(-\dfrac{q}{p^3}\)
- C \(\dfrac{q}{p}\)
- D \(-\dfrac{q}{p^2}\)
Answer & Solution
Correct Answer
(B) \(-\dfrac{q}{p^3}\)
Step-by-step Solution
Detailed explanation
Given \(p = \dfrac{dy}{dx}\), we have \(\dfrac{dx}{dy} = \dfrac{1}{p} = p^{-1}\). Differentiating both sides with respect to \(y\) using the chain rule: \(\dfrac{d^2x}{dy^2} = \dfrac{d}{dy} \left( p^{-1} \right) = \dfrac{d}{dx} \left( p^{-1} \right) \cdot \dfrac{dx}{dy}\)…
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
- \(\lim\limits_{x \to 0}\dfrac{(1 - \cos 2x)(3 + \cos x)}{x\tan 4x}\) is equal to:COMEDK 2026 Easy
- If \(f(x)\) satisfies the relation \(2 f(x)+f(1-x)=x^{2}\) for all real \(x\), then \(f(x)\) isCOMEDK 2021 Medium
- If \(A=\left[\begin{array}{ccc}1 & -1 & 1 \\ 2 & 1 & -3 \\ 1 & 1 & 1\end{array}\right], 10 B=\left[\begin{array}{ccc}4 & 2 & 2 \\ -5 & 0 & \alpha \\ 1 & -2 & 3\end{array}\right]\) a is the inverse of \(A\), then the value of \(\alpha\) isCOMEDK 2020 Medium
- If the circles \(x^{2}+y^{2}-2 x-2 y-7=0\) and \(x^{2}+y^{2}+4 x+2 y+k=0\) cut orthogonally, then the length of the common chord of the circles isCOMEDK 2020 Hard
- If \((\sqrt{3}+i)^{100}=2^{99}(a+i b)\), then \(a^{2}+b^{2}\) is equal toCOMEDK 2021 Medium
- \(11^{3}+12^{3}+13^{3}+\ldots . .+20^{3}\) isCOMEDK 2015 Medium
More PYQs from COMEDK
- If \(A=\left[\begin{array}{ll}1 & 0 \\ 1 & 1\end{array}\right]\) and \(A^{8}=a A+b I\), then \((a, b)=\)COMEDK 2015 Medium
- Given are 4 pairs of covalent molecules. Identify the pair in which both molecules have the same shape.COMEDK 2025 Medium
- If \(\tan \theta+\tan 4 \theta+\tan 7 \theta=\tan \theta \tan 4 \theta \tan 7 \theta\) then the general solution isCOMEDK 2018 Medium
- Calculate the molar conductance of \(0.025 \mathrm{M}\) aqueous solution of calcium chloride at \(25^{\circ} \mathrm{C}\). The specific conductance of calcium chloride is \(12.04 \times 10^{-2} \mathrm{Sm}^{-1}\)COMEDK 2022 Easy
- For all \(n \in N, 2 \cdot 4^{2 n+1}+3^{3 n+1}\) is divisible byCOMEDK 2017 Medium
- A simple pendulum is suspended from the
ceiling of a lift. When the lift is at rest its time
period is T. With what acceleration should the
lift be accelerated upwards in order to reduce
its period to T / 2 ?
(g is acceleration due to gravity)COMEDK 2018 Easy