Solve `(dx)/(d t) = (t(2 log t + 1))/(sin x + x cos x)`

(d)/(dx) [(x)/(2) + 1/2 log | sin x + cos x|]=

Find (dy)/(dx) if x =a ( cos t + t sin t ), y = a ( sin t - t cos t).

int (cos x)/( sin x log sin x)dx=

If x and y are connected parametrically by the equations given in Exercises 1 to 10, without eliminating the parameter, Find (dy)/(dx) . x= a(cos t+ log tan (t)//(2))y= a sin t .

1. If x = at ^(2) , y = 2 at then (dy)/(dx) at t =1 is A 2 If x =cos theta, y = sin theta then (dy)/(dx) at theta = (pi)/(4) is B 3 If x =1 - cos theta, y = sin theta , then (dy )/(dx) at theta = (pi)/(6) is C 4 If x = log sin theta, y = tan theta then (dy)/(dx) at theta = (pi)/(4) is D. The ascending order of A,B,C,D is

Find the derivative of the w.r.t.x log [(sin (log x ) + x log x log (log x)]

The curve represented by x=3 (cos t + sin t ) ,y =4 (cos t -sin t ) is