How to find the derivative of this function

[rishi kesh]

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.

 

[PeroK]

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?

 

[rishi kesh]

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 !

 

[timetraveller123]

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)

 

[PeroK]

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 $1-x$

 

[rishi kesh]

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.

 

[PeroK]

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.

 

[rishi kesh]

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.

 

[PeroK]

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.