Find the value of $\frac{d^2y}{dx^2}$ when $x = 1$ for the equation $x^2y - 4x = 5$. It is known that $\frac{dy}{dx} = \frac{4 - 2xy}{x^2}$.

Answered: d²y when x = 1 for the equation x²y –…

Calculus: Early Transcendentals

8th Edition

ISBN:9781285741550

Author:James Stewart

Publisher:James Stewart

Chapter1: Functions And Models

Section: Chapter Questions

Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...

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Find the value of $\frac{d^2y}{dx^2}$ when $x = 1$ for the equation $x^2y - 4x = 5$. It is known that $\frac{dy}{dx} = \frac{4 - 2xy}{x^2}$.

Expert Solution

Step 1

Given that the equation:

$x^{2} y - 4 x = 5$

Differentiate the given function with respect to “x” then,

$\begin{matrix} \frac{d}{d x} (x^{2} y - 4 x) = \frac{d}{d x} 5 \\ x^{2} \frac{d y}{d x} + y \frac{d}{d x} x^{2} - 4 \cdot 1 = 0 \\ x^{2} \frac{d y}{d x} + 2 x y - 4 = 0 \\ x^{2} \frac{d y}{d x} = 4 - 2 x y \\ \frac{d y}{d x} = \frac{4 - 2 x y}{x^{2}} . . . . . . . . . (1) \end{matrix}$

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