If `x=acostheta,y=bsintheta,` then prove that `(d^3y)/(dx^3)=(3b)/(a^3)cos e c^4thetacotthetadot`

If x=acostheta , y=bsintheta then eliminate theta .

If x=acostheta,y=bsintheta," then"(d^(3)y)/(dx^(3)) is equal to

If x=a cos theta,y=b sin theta, show that (d^(2)y)/(dx^(2))=-(b^(4))/(a^(2)y^(3))

If x=a sec theta,y=b tan theta, prove that (d^(2)y)/(dx^(2))=-(b^(4))/(a^(2)y^(3))

If x=a(1-cos^(3)theta),y=as in^(3)theta, prove that (d^(2)y)/(dx^(2))=(32)/(27a) at theta=(pi)/(6)

If x=cos theta,y=s in^(3)theta, prove that y(d^(2)y)/(dx^(2))+((dy)/(dx))^(2)=3s in^(2)theta(5cos^(2)theta-1)

If x=cos theta,y sin^(3)theta, prove that y(d^(2)y)/(dx^(2))+((dy)/(dx))^(2)=3sin^(2)theta(5cos^(2)theta-1)

If y=A cos x+B sin x, then prove that : (d^(4)y)/(dx^(4))=y

If y=log(sin x), prove that (d^(3))/(dx^(3))=2cos x csc^(3)x

If x=a cos^(3)theta,y=b sin^(3)theta, find (d^(3)y)/(dx^(3)) at theta=0