y=-sin(sinx)cosxy=−sin(sinx)cosx
dy/dx=d/dx(-sin(sinx)cosx)dydx=ddx(−sin(sinx)cosx)
Using formula d/dx(u.v)=v d/dx(u)+u d/dx(v)ddx(u.v)=vddx(u)+uddx(v)
dy/dx=cosxd/dx(-sin(sinx))+(-sin(sinx))d/dx(cosx)dydx=cosxddx(−sin(sinx))+(−sin(sinx))ddx(cosx)
Using Chain Rule Formula
d/dx(f(g(x)))=f'(g(x)).d/dx(g(x))
dy/dx=cosx(-cos(sinx)d/dx(-sin(sinx))+(-sin(sinx))(-sinx)
dy/dx=cosx(-cos(sinx)cosx)+(-sin(sinx))(-sinx)
dy/dx=-cos^2xcos(sinx)+sinxsin(sinx)
(d^2y)/dx^2=d/dx(dy/dx)
(d^2y)/dx^2=d/dx(-cos^2xcos(sinx)+sinxsin(sinx))
(d^2y)/dx^2=-cos^2xd/dx(cos(sinx))+cos(sinx)d/dx(-cos^2x)+sin(sinx)d/dx(sinx)+sinxd/dx(sin(sinx))
(d^2y)/dx^2=-cos^2x(-sin(sinx)d/dx(sinx))+cos(sinx)(-2cosx(-sinx))+sin(sinx)cosx+sinxcos(sinx)d/dx(sinx)
(d^2y)/dx^2=cos^3xsin(sinx)+2sinxcosxcos(sinx)+sin(sinx)cosx+sinxcos(sinx)cosx
(d^2y)/dx^2=cos^3xsin(sinx)+3sinxcosxcos(sinx)+sin(sinx)cosx
(d^2y)/dx^2=cosx[sin(sinx)(cos^2x+1)+3sinxcos(sinx)]