I need help with no 2 , 3 and 4

1. Use the method of implicit differentiation to determine the derivatives of the following functions: (a) xsin y + ysin x = 1 (5) (b) tan(x- y)= 1+x (5) (c ) vx+ yex'+y* (5) (d) y + xcosy = xy (5) (e) 2y + cot(xy! )= 3xy (5) 2. Find the number "c" that satisfy the Mean Value Theorem (M.V.T.) on the given intervals. (a) f(x)=e". [o. 2] (5) (b) f (x ) = *[1.x] x+2 (5) 3. Determine the equation of the tangent and normal at the given points: (a) y+ xcosy = xy. 1. (5) (b) h(x)=atx=1. Vx- +1 (5) 4. Find the derivative of f(x) - f (v +2)v (5) 5. Find the derivative of the following functions using the appropriate rules for differentiation. Simplify your answer: F(x) = [vr + ldt