Calculus (derivative) help!!!?

Question

I cant figure any of these out!!
1)Find dy/dx if y=sin(x+y)
2)differentiate: y=csc^2(x)+cot^2(x)
3)differentiate: y=sin^2(t)-cos^2(t)
4)Find dy/dx if (x^2)-(y^2)=2xy
5)Find dy/dx for the equation (x^3)-(2(x^2)y)+3xy^2=38
6)Find dy/dx, then evaluate the derivative at the point (0,2): (x^2)-(2xy)=(y^2)-4
7)Find an equation for the tangent line to the graph of f(x)=√(x+1) at the point where x=3.8)
8)Find f '(x) for f(x)=2(x^2+5)^7

Answer 1

The genera idea on 1, 4, 5, and 6 is implicit differentiation. Differentiate both sides of the equation and use the chain rule. Get an expression for y' in terms of both x and y.

Anyhow, I suggest you re-ask this as a bunch of different questions. 8 of them crammed together is pretty overwhelming.