Questions about Calculus (請解釋)

1.Let f(t)=sin(2*22/7*t). Find the points where the tangent of the graph of f is horizontal.
2.Find the derivative of the following functions:
(a) f(x)=1+x+(x^2)/2 +(x^3)/6 +(x^4)/24 .
(b) f(x)=cot*x
(c) f(x)=(x^2) arcsin *x
3.Find the second derivative of f(x)=(sin*x)/(1-cos*x)
4.Find d/dt [t d/dt (cos*t^2)]
5.Given that y=u^2, u=sec*x, x=(1+t)^2 .Express dy/dt in terms of t.
6.The surface area of a sphere with radius r is given by S=4*22/7*r^2 . Find the radius at which the rate of change of S w.r.t. r is 2.
(a)1/(4*22/7)
(b)1/(2*22/7)
(c)1/(22/7)
(d)1
(e)2