Derivatives of both sides of x, 1=-4t*dt/dx, dt/dx=- 1/4t.
dy/dx=d( 1+sint)/dx*[ 1+e^( 1/( 1+sint))]
=cost*dt/dx*[ 1+e^( 1/( 1+sint))]
=-cost/4t*[ 1+e^( 1/( 1+sint))]