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

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

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 w(x,y,z) =x^(2) + y^(2)+ z^(2), x=e^(t), y=e^(t) sin t and z=e^(t) cos t , find (dw)/(dt) .

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

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

if x=log_(e)t,t>0 and y+1=t^(2) then (d^(2)y)/(dx^(2))

If x=e^t sin t , y=e^t cos t , t is a parameter , then (d^2y)/(dx^2) at (1,1) is equal to

If x=e^t sin t , y=e^t cos t , t is a parameter , then (d^2y)/(dx^2) at (1,1) is equal to