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Math Help - Some assorted questions (includes implicit differentiation, inverse trig funcs, etc)

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    Some assorted questions (includes implicit differentiation, inverse trig funcs, etc)

    Im sure this is easy for most of you math wizards, but its really difficult for me to identify which laws and stuff to use and when.

    For example:

    1)

    xarctany

    if I want to differentiate that, do I have to use multiplication rule? what would that differentiate out to?

    I also have a lot of trouble with radians and points that contain pi. I've never been able to wrap my head around it. if I have the point (-pi/4, 1) and need to plug that point into an equation after ive solved for dy/dx how does it work? if i plug (-pi/4) into say cosin(x) what does it come out to? and whats an easy way to understand this so i can apply it to all trig functions? I just dont get how pi works in this context.

    2) How do I find the extreme values (abs and local) of a function? especially one that uses pi in the given range. is there a good online tutorial you could point me to? i dont really want the problem simply done for me i want to try and understand it

    Thanks for any help. I really appreciate it as I am struggling here
    Last edited by heidecker; July 10th 2012 at 08:48 PM.
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  2. #2
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    Re: Some assorted questions (includes implicit differentiation, inverse trig funcs, e

    Quote Originally Posted by heidecker View Post
    xarctany

    if I want to differentiate that, do I have to use multiplication rule?
    Assuming y is a function of x and you want to differentiate with respect to x, then the product rule yes, but also the chain rule because arctan y is a composite function where y is the inner function of x.

    Just in case a picture helps...



    ... where (key in spoiler) ...

    Spoiler:


    ... is the chain rule. Straight continuous lines differentiate downwards (integrate up) with respect to the main variable (in this case x), and the straight dashed line similarly but with respect to the dashed balloon expression (the inner function of the composite which is subject to the chain rule).

    But this is wrapped inside the legs-uncrossed version of...



    ... the product rule, where, again, straight continuous lines are differentiating downwards with respect to x.


    Quote Originally Posted by heidecker View Post
    is there a good online tutorial you could point me to? i dont really want the problem simply done for me i want to try and understand it
    Pauls Online Notes : Calculus I


    __________________________________________________ __________

    Don't integrate - balloontegrate!

    Balloon Calculus; standard integrals, derivatives and methods

    Balloon Calculus Drawing with LaTeX and Asymptote!
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