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    Given that
    x=sec²y+tany
    Show that
    dy/dx = cos²y/(2tany+1)

    I know it's an easy question and I would be able to do it if it started y=... but it's confusing me =(
    Thanks in advance ^-^
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    Just use the result that dy/dx is one over dx/dy. Then it's a standard differentiation (albeit with the usual letters swapped) followed by a flip.
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    you have to use implicit differentiation:

    x=sec2y+tany
    1=2(sec(y))(sec(y)(tan(Y))dy/dx + sec2y(dy/dx)
    1=2(sec2y)(tany)dy/dx + sec2y(dy/dx)
    1=(dy/dx)[(sec2y) + (2tany + 1)

    Thus dy/dx = cos2y/(2tany+1)

    Alternatively, you can just do dx/dy and then inverse what you get.
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    Thanks heaps both of you ^-^
    -adds to rep-
 
 
 
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