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Question #1. Differentiate 1. f(x) = 4 -23 3. f(x) = x3 vx5 + 6.x. 2. f (x) = ( 24.). 4. f(x) = 12(2x + 1)2/3(3x - 4) 5/4. Question #2. Find - dy du and - dy du' dx 15 1. y = = u+1 7/3 and u = 2x + 1. 3. y = = u _ j and u = 1+ vx. 2. y = u(u + 1) and u = x3 - 2x. Question #3. Find- dy . 1. y = V2u + 5 and u = x2 - x. 1 2. y = - and u = 5 + 3x. u2 + u Question #4. Find the equation of the tangent line to the graph of: 1. y = vx2 + 3x at (1, 2). 2. y = xv2x + 3 at (2, 0). Question #5. Use implicit differentiation to find- dx i. xy' + x sin(y) = 4. iii. 3 +xy + 4y? = 6. ii. 1 +x = sin(xy?). Question #6. Find the equation of the tangent line: i. x2 + xy + y? = 3 at (1, 1). ii. x2 + 2xy - y? + x = 2 at (1, 2). Question #7. Find - dy dx2 = y" i. 9x2 + y? = 9. ii. Vi + Vy = 1. Question #8. Each side of a square is increasing at rate 6 m/s. What is the rate in which the area is increasing when the area is 16 cm