1. Not finding help here? Sign up for a free 30min tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

More differentiation troubles

  1. Jun 20, 2004 #1
    Differentiate y = (1 - sin x) / (1 + sin x)

    i know the answer is - 2 cos x / 1 + sin x

    Again, i just cant do the working
  2. jcsd
  3. Jun 20, 2004 #2
    Your answer is wrong. The denominator should be squared.

    You can either use the product and chain rule on the equivalent expression (1 - sin x)(1 + sin x)^-1, or you can use the quotient rule.

    The latter is more straightforward, so let's go with that one.

    The quotient rule is:

    [tex]\frac {d}{dx} \left[ \frac {f(x)}{g(x)} \right] = \frac {g(x)f'(x) - f(x)g'(x)}{g(x)^2}[/tex]

    Be careful with that thing, it's dangerous! It's sharp and pointy and you shouldn't run while holding it. And it matters which function is on the top, so make sure you know which is f(x) and which is g(x) before using it.

    Applying the quotient rule yields:

    [tex]\frac {d}{dx} \frac {1 - \sin x}{1 + \sin x} = \frac {(1 + \sin x)(-\cos x) - (1 - \sin x)(\cos x)}{(1 + \sin x)^2}[/tex]

    Factor out -cos x:

    [tex]= -\cos x \left[ \frac{1 + \sin x + 1 - \sin x}{(1 + \sin x)^2} \right] [/tex]


    [tex]= \frac{-2 \cos x}{(1 + \sin x)^2}[/tex]
  4. Jun 20, 2004 #3
    god dammit, stupid textbook
    yeh thanks for that, i got that answer too, i was wondering where i went wrong as i got (1 + sin x) squared on the bottom too, but the text got 1 + sin x on the bottom, arggh. thanks for that
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?

Similar Discussions: More differentiation troubles
  1. More QM trouble (Replies: 5)