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)