[" 2"quad x=log_(e)t+sin t,y=e^(t)+cos t],[" io."]

Find dy/dx : x = log t+ sin 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 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)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)

x=e^t (sin t + cos t ),y=e^t(sin t -cos t)

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

If x = e^(t) sin t and y = e^(t) cos t, t is a parameter , then the value of (d^(2) x)/( dy^(2)) + (d^(2) y)/(dx^(2)) at t = 0 , is :

Find dy/dx x=e^t (sin t + cos t ),y=e^t(sin t -cos t)