Calculating dy/dx for Inverse Sine Functions

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Homework Help Overview

The discussion revolves around calculating the derivative of an inverse sine function, specifically involving the expression Y = sin^(-1)(x + sin^(-1)(√(1 - x^2))). Participants are exploring the differentiation of this composite function within the context of calculus.

Discussion Character

  • Exploratory, Mathematical reasoning, Assumption checking

Approaches and Questions Raised

  • Some participants attempt to clarify the function's notation and structure, while others suggest using the chain rule for differentiation. There are questions regarding the appropriateness of the problem's classification and its relation to differential equations.

Discussion Status

The discussion is ongoing, with participants providing insights into the function's setup and differentiation approach. A moderator has indicated that the thread should remain focused on homework help, suggesting that further guidance should wait until the original poster provides an attempt at the problem.

Contextual Notes

There is a note from a moderator emphasizing the importance of adhering to homework help guidelines, indicating that the problem may be part of a textbook exercise or independent study.

Prasad Nemade
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Y= sin^(-1)⁡〖x+ sin^(-1)⁡√((1-x^2 ) 〗
Please show steps for it...
 
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Since this problem has nothing to do with "differential equations", I am moving it.
 
Prasad Nemade said:
Y= sin^(-1)⁡〖x+ sin^(-1)⁡√((1-x^2 ) 〗
Please show steps for it...
There are some funny looking symbols in there. I will assume that the function is
[tex]y= sin^{-1}(x+ sin^{-1}(\sqrt{1- x^2}))[/tex]

Let [itex]u(x)= 1- x^2[/itex], [itex]v(u)= \sqrt{u}= u^{1/2}[/itex], and [itex]w(v)= sin^{-1}(v)[/itex]. Then use the chain rule.
 
Moderator's note:

This looks like homework, or at the very least a textbook-style problem. Even if it's for independent study and not assigned coursework, this thread should in the Homework & Coursework Questions forums.

I am moving it to the Calculus & Beyond homework forum. Please note that the usual rules for homework help are in effect.

EDIT: in case it isn't clear -- we should let the OP reply with an attempt at solving this before offering further help.
 
Last edited:

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