Question

If y = a sin x + y sin a, find d^2 y / dx^2 and da/dy.

Answer 1

y=a.sinx+ysina
y-ysina=a.sinx
y (1-sina)=a.sinx
y={a/(1-sina)} sinx
now differentiate w.r.t x
dy/dx={a/(1-sina)} cosx
again differentiate
d^2/dx^2={a/(1-sina)}(-sinx)

y=asinx+ysina
differentiate w.r.t a
dy/da=sinx+dy/da.sina+y.cosa
dy/da (1-sina)=sinx+ycosa
dy/da=(sinx+ycosa)/(1-sina)
so, da/dy=(1-sina)/(sinx+ycosa)