" 11."x=log_(e)t,y=e^(t)+cos t

Equations of the tangent and normal to the curve x=e^(t) sin t, y=e^(t) cos t at the point t=0 on it are respectively

If x=e^(t)sin t,y=e^(t)cos t then (d^(2)y)/(dx^(2)) at x=pi is

Let U(x,y,z) = xyz, x=e^(-t), y=e^(-t) cos t, z= sin t, t in R . Find (dU)/(dt) .

If x = e^(t)sint, y =e^(t)cost then (d^2y)/(dx^2) at t = pi is

If x = e ^(t ) sin t, y = e ^(t) cos t, then (d ^(2) y )/(dx ^(2)) at t = pi is

The tangent to the curve given by : x=e^(t)cos t, y=e^(t) sin t at t=(pi)/(4) makes with x-axis an angle :

Show that the function y=f(x) defined by the parametric equations x=e^(t)sin(t),y=e^(t).cos(t), satisfies the relation y''(x+y)^(2)=2(xy'-y)

Show that the function y=f(x) defined by the parametric equations x=e^(t)sin(t),y=e^(t).cos(t), satisfies the relation y''(x+y)^(2)=2(xy'-y)

if x=e^(t)sin t and y=e^(t)cos t , then prove that (x+y)^(2)(d^(2)y)/dx^(2)=2(xdy/dx-y) .