Calculus and vectors (DERIVATIVES OF TRIG & EXPONENTIAL FUNCTIONS)

Please show all work leading to answer

1. Determine an equation for the tangent at the point with the given x-coordinate for each of the following functions:

a)f(x)=sinx,x=3 b)f(x)=sin2x+cosx,x=2

2. Determine the equation of the tangent to the graph of y=xcos2x at x=2

3. Using implicit differentiation, find dxdy of:

a)x3+xyy2=12 b)3xy+2x43y3=5y

4. Differentiate the following:

a)y=e2x+3 b)y=2x+3ex c)y=43x2 d)f(x)=sinx1+cosx e)y=cos(sin2x)

f)y=2x3sinx3xcosx

5. Find the derviative of the following functions:

a)f(x)=(sinx+tanx)4 b)f(x)=xtan(2x1)