How to find the derivative of this function

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Homework Help Overview

The discussion revolves around finding the derivative of the function y = √[(1 - sinx)/(1 + sinx)], which is presented as an exercise problem from a textbook. Participants note that the original poster has not yet covered the chain rule and requests guidance using basic derivative rules.

Discussion Character

  • Exploratory, Conceptual clarification, Mathematical reasoning

Approaches and Questions Raised

  • Participants discuss various methods to manipulate the expression, including replacing the square root with a power of 1/2 and considering the implications of the quotient form. There are suggestions to multiply the numerator and denominator by specific terms to simplify the expression.

Discussion Status

The discussion is active, with participants offering different strategies for approaching the problem. Some have provided hints about manipulating the terms within the square root and exploring standard functions for derivatives. There is no explicit consensus on a single method, but several productive lines of inquiry are being explored.

Contextual Notes

Participants note the constraint of not using the chain rule, which may limit the approaches available for solving the problem. The original poster expresses difficulty in reaching the solution despite attempts to manipulate the expression.

rishi kesh
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Homework Statement


How do we find the derivative of function:
y= √[(1-sinx)/(1+sinx)]
This is the exercise problem from my textbook. I have not covered chain rule yet. So please you basic derivative rules to solve it.

Homework Equations


Here is the answer of derivative given in my textbook: secx(tanx-secx)

The Attempt at a Solution


I have tried replacing square root by power of 1/2 but can't reach to the answer.
 
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rishi kesh said:

Homework Statement


How do we find the derivative of function:
y= √[(1-sinx)/(1+sinx)]
This is the exercise problem from my textbook. I have not covered chain rule yet. So please you basic derivative rules to solve it.

Homework Equations


Here is the answer of derivative given in my textbook: secx(tanx-secx)

The Attempt at a Solution


I have tried replacing square root by power of 1/2 but can't reach to the answer.

Can you see a way to get rid of the square root?
 
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PeroK said:
Can you see a way to get rid of the square root?
Hi! Please give me a little bit of intuition about this. I will solve the rest. Thanks in advance !
 
rishi kesh said:
Hi! Please give me a little bit of intuition about this. I will solve the rest. Thanks in advance !
think of manipulating the terms within the square root itself
(1 - sin^2x = cos ^2x)
 
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rishi kesh said:
Hi! Please give me a little bit of intuition about this. I will solve the rest. Thanks in advance !
Whenever you have an expression of the form
##\frac{1+x}{1-x}##

you should think about multiplying top and bottom by ##1+x## or ##1-x##
 
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PeroK said:
Whenever you have an expression of the form
##\frac{1+x}{1-x}##

you should think about multiplying top and bottom by ##1+x## or ##1-x##
Hi! I am sorry i tried but i couldn't solve it . I would greatly appreciate your help.
 
rishi kesh said:
Hi! I am sorry i tried but i couldn't solve it . I would greatly appreciate your help.
Multiply top and bottom by ##1-\sin x## and see what comes out.
 
PeroK said:
Multiply top and bottom by ##1-\sin x## and see what comes out.
Here is a picture of what I've solve. Please tell me if its correct.
 

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rishi kesh said:
Here is a picture of what I've solve. Please tell me if its correct.
Looks good so far. If you can't use the chain rule, you could look for some standard functions that you know the derivative for.

PS I forgot you could use the quotient rule, although I always think of that as the product rule plus the chain rule.
 
Last edited:

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