Posted by T.Gracken on October 24, 2002 at 16:45:15:
In Reply to: HELP! posted by erin on October 24, 2002 at 13:00:51:
: how do i do this problem? FIND: d^2y/dx^2 in terms of x and y: xsiny=3
: I found the first dy/dx and it=-siny/xcosy, but I'm not sure how to go about doing the rest. Please e-mail me if you can help
you have done most of the work already.
that is, you determined the first derivative with respect to x...
dy/dx = -sin(y)/[x*cos(y)]
you can now either use the quotient rule on the right to get the second derivative ...or
a little trig identity gives
dy/dx = -tan(y)/x
so d2y/dx2 = -[x*sec2(y)*(dy/dx) - tan(y)]/x2
substitute -tan(y)/x into dy/dx [you already had this from above] and simplify.
hope that helps.
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