frac{d^2 x}{d y^2} equals | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(D) We know that $\frac{d x}{d y} = \frac{1}{d y / d x} = \left(\frac{d y}{d x}\right)^{-1}$.Now,differentiate both sides with respect to $y$:$\frac{d

Vedclass · Accepted Answer

$-\left(\frac{d^2 y}{d x^2}\right)\left(\frac{d y}{d x}\right)^{-3}$

Vedclass · Answer

(D) We know that $\frac{d x}{d y} = \frac{1}{d y / d x} = \left(\frac{d y}{d x}\right)^{-1}$.Now,differentiate both sides with respect to $y$:$\frac{d^2 x}{d y^2} = \frac{d}{d y} \left[ \left(\frac{d y}{d x}\right)^{-1} \right]$.Using the chain rule,we have:$\frac{d^2 x}{d y^2} = \frac{d}{d x} \left[ \left(\frac{d y}{d x}\right)^{-1} \right] \cdot \frac{d x}{d y}$.Applying the power rule:$\frac{d^2 x}{d y^2} = -\left(\frac{d y}{d x}\right)^{-2} \cdot \frac{d^2 y}{d x^2} \cdot \frac{d x}{d y}$.Since $\frac{d x}{d y} = \left(\frac{d y}{d x}\right)^{-1}$,we substitute this into the expression:$\frac{d^2 x}{d y^2} = -\left(\frac{d y}{d x}\right)^{-2} \cdot \frac{d^2 y}{d x^2} \cdot \left(\frac{d y}{d x}\right)^{-1}$.Combining the powers of $\frac{d y}{d x}$:$\frac{d^2 x}{d y^2} = -\left(\frac{d^2 y}{d x^2}\right) \left(\frac{d y}{d x}\right)^{-3}$.

$\frac{d^2 x}{d y^2}$ equals

Similar Questions

The function $y=e^{kx}$ satisfies $(\frac{d^2y}{dx^2}+\frac{dy}{dx})(\frac{dy}{dx}-y)=y\frac{dy}{dx}$. It is valid for

If $f(x) = \sin x \cdot \sin 2x \cdot \sin 3x$ and $f''(x) = a(\sin bx) + c(\sin dx) + e(\sin kx)$,then the value of $(a+c+e) - (b+d+k)$ equals

Let $y = \log_8 \left( \frac{1-x^2}{1+x^2} \right)$ for $-1 < x < 1$. Then at $x = \frac{1}{2}$,the value of $225(y' - y'')$ is equal to:

$y = a \cos x + (b + 2x) \sin x \Rightarrow y^{\prime \prime} + y = $

If $x = A \cos 4t + B \sin 4t$,then $\frac{d^2x}{dt^2} = $

Vedclass Test Series

Exam Paper Generator

Online Exam Module