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Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
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**Topic: Calculus: Derivatives**

In this example, we are given the derivative of a function \(y\) with respect to \(x\).

The handwritten formula presented is:

\[ \frac{dy}{dx} = \frac{1 \cdot y^2}{1 + x^2} \]

This equation represents the derivative \(\frac{dy}{dx}\), indicating the rate of change of \(y\) with respect to \(x\). The numerator consists of the product of 1 and \(y^2\), and the denominator is the sum of 1 and \(x^2\). This type of equation might appear in problems involving differential equations or in the study of specific forms of functions where understanding how one variable changes in relation to another is necessary.

Remember to always simplify your expressions where possible and apply appropriate rules of differentiation when handling more complex equations.
Transcribed Image Text:**Topic: Calculus: Derivatives** In this example, we are given the derivative of a function \(y\) with respect to \(x\). The handwritten formula presented is: \[ \frac{dy}{dx} = \frac{1 \cdot y^2}{1 + x^2} \] This equation represents the derivative \(\frac{dy}{dx}\), indicating the rate of change of \(y\) with respect to \(x\). The numerator consists of the product of 1 and \(y^2\), and the denominator is the sum of 1 and \(x^2\). This type of equation might appear in problems involving differential equations or in the study of specific forms of functions where understanding how one variable changes in relation to another is necessary. Remember to always simplify your expressions where possible and apply appropriate rules of differentiation when handling more complex equations.
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