Assignment 3 (Chapter 2: Differentiation) 1

Assignment 3 (Chapter 2: Differentiation) Due date: Wednesday 21st May 2008

Q1. Find an equation for the line perpendicular to the tangent to the curve

122 +−= xxy at the point (0,1).

Q2. Given uy ln= and 2)2ln2(tan xxu += , find dxdy .

Q3. Find )(xf ′ :

1) 22 )ln()( xxexf +=

2) 4 )2sin(2)( xxf +=

3) ⎟⎟⎠

⎞⎜⎜⎝

⎛+

=12

tan)(xxxf

4) )]cos[ln(sin)( 4xxf =

Q4. Use implicit differentiation to find y′ :

1) 222)( yxyxx +=+ 2) π=+ )sec(xyx 3) xye yx =− ln

2 Q5. Find the tangent line to the curve ππ =+ yxy cos2 at the point )2/,1( π .