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    given that

    x= sec^2 y + tan y

    show that dy/dx = (cos^2 y)/ (2tany +1)

    kay I know I have to differentiate it then flip it over to make dy/dx isntead of dx/dy, but I can't differentiate it
    can anyone help
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    find dx/dy instead of dy/dx

    dx/dy = secytant*secy+ secytany*secy + sec^2 y
    (using product rule on sec^2 y ie. (sec y*sec y))

    dx/dy = (sec^2 y)(2tany + 1) (factorising out sec^2 y)

    dx/dy = (2tany + 1)/ (cos^2 y) (using sec^2 y = (1/cos^2 y)

    so dy/dx = (cos^2 y)/(2tany + 1) (using dy/dx = 1/(dx/dy))
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    how did you get the first line??

    does * mean multiplied by?
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    (Original post by sarax)
    given that

    x= sec^2 y + tan y

    show that dy/dx = (cos^2 y)/ (2tany +1)

    kay I know I have to differentiate it then flip it over to make dy/dx isntead of dx/dy, but I can't differentiate it
    can anyone help
    x = (secy)^2 + tany
    => 1 = 2secy.secy.tany.dy/dx + sec^2y.dy/dx
    => 1 = dy/dx(2sec^2y.tany + sec^2y)
    => dy/dx = 1/(2sec^2y.tany + sec^2y)
    => dy/dx = 1/sec^2y.(2tany+1)
    => dy/dx = cos^2y/(2tany+1)
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    (Original post by sarax)
    how did you get the first line??

    does * mean multiplied by?
    yes
 
 
 
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