- #1
Ande Yashwanth
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Find derivative of y=✓{x+✓[y+✓(x+...)]}infinite.
Here root comes for total inter terms
Here root comes for total inter terms
[tex]y= \sqrt{x+ \sqrt{y+ \sqrt{x+ \cdot\cdot\cdot}}}[/tex] is clearly the same as [tex]y= \sqrt{x+ \sqrt{y+ y}}= \sqrt{x+ \sqrt{2y}}[/tex].Ande Yashwanth said:Find derivative of y=✓{x+✓[y+✓(x+...)]}infinite.
Here root comes for total inter terms
Differentiation of infinite series is the process of finding the derivative of each term in an infinite series. It involves finding the rate of change of the terms in the series with respect to a given variable.
Differentiation of infinite series is important because it allows us to analyze and understand the behavior of infinite series. It also helps in solving problems involving infinite series in various fields such as physics, engineering, and economics.
The formula for differentiating an infinite series is similar to the formula for differentiating a finite series. Each term in the series is differentiated individually using the power rule, product rule, quotient rule, or chain rule, depending on the form of the term.
No, not all infinite series can be differentiated. Some series may not have a derivative that exists or is well-defined. It is important to check for convergence and other conditions before attempting to differentiate an infinite series.
Differentiation and integration are inverse operations. Therefore, the process of finding the derivative of an infinite series is closely related to finding the antiderivative, or integral, of the same series. This relationship is known as the Fundamental Theorem of Calculus.