I'm having trouble with part of a FP2 question.
z=sin x implies (dz/dx)=cosx
(dy/dx)= (dy/dz) * cosx
(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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Last edited by oli949; 28-11-2011 at 21:28.
- 28-11-2011 21:15
- 28-11-2011 21:36
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