I have a test coming up and these are a few problems giving me a little trouble, if someone could help solve these and walk me through the steps it would be greatly appreciated...

1.) Let n be a fixed positive integer. Prove that:

d/dx ([sin^n](x)cos(nx)) = n[sin^n-1](x)cos((n+1)x)

(hint: the identity cos(A+B)=cosAcosB+sinAsinB will be useful)

2.) Let C denote the curve given by the equation:

y^3 - xy^2 + cos(xy)=2

Employ implicit differentiation to calculate the slope of the tangent line to C at point (0,1)

3.) Let C denote the parametric curve determined by the equations

x(t)= (t+1)^2/3 y(t)= tsec(t) -π/2≤x≤π/2

i) compute x'(t) and y'(t)

ii) compute dy/dx in terms of the parameter t

iii) calculate the slope of the tangent to C at the point (1,0)