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Substitution and second order differentials watch

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    I'm having trouble with part of a FP2 question.

    z=sin x implies (dz/dx)=cosx

    (dy/dx)= (dy/dz) * cosx

    And
    (d²y/dx²)= (d²y/dz²) * cos²x – (dy/dz) * sinx

    How has the answer to (d²y/dx²) been figured out? Any help would be greatly appreciated. Thanks

    PS: It's the "cos²x" part I'm struggling to understand.
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    dy/dx= dy/dz dz/dx chain rule
    d2y/dx2= d/dx(dy/dx)= d/dx (dy/dz dz/dx) by definition

    use product rule to get

    d2y/dx2= dy/dz d2z/dx2 + d/dx(dy/dz) dz/dx
    = dy/dz d2z/dx2 + d/dz(dy/dz) dz/dx )dz/dx by chain rule
 
 
 
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Updated: November 28, 2011

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