Question

1. Find f(x) f(x) = 27 {rewrite first-leave answer as a radical) 3 +1 2. Find f'() 2. Find f'(x) f(x) = x {rewrite first; 3. Find f(x) f(x) = 21n(1+3x2) + 3e(4433) 4. Find f'(x) for f(x) = x2\n(x3+1) {Note: uses product rule f'g+g'f} dir dx 2x+1 f'g-g'ſ 5. Find {Note: uses quotient rule }

Answer 1

1. If f(x) = 2 (x343 get : differentiate with respect to x, f'(x) = 2. (x)2/3-1 (x)/ 4 3 x 2. f(x) = +1 X4 3. x4 +1 we gett f(x) = differentiate with respect to f'(x) = 3(-4) x-4-1 f'(x) = to - 12x-5 f'(x) = - 12 ws 3 e(4+3x²) 3. f(x)= 2 ln (1+3x² + 3 let 1+ 3x² = t and 4 + 3x² = ti differentiate with respect to x, we get:

f'(x) = 2 . a la en(t). d (1+3x² + 3 det. d (4+32²) da dn 62 (6x) - 2. +3. et. Put the values of t and to + we get f'(x) = + 122 It 3x² 18x + 3x²) GR (32+ Bechise) 4. f(x) = x² lin(x3 + 1) differentiate with respect to x, using product date, we get f'owy = x. d (len (x3 + x)) + ln (x3 + 1) d x2 . f'(x) = x² 1 3x2 + ln x + 1). 2x x3 + 1 37 x + + 2x ln (+1) f'(x) = 3x4 + 2x ln (2+1) x² +1 5 2x+1 e Using quotient rule, we get:

= (2x+1) a (x²) - x h (2x+1) (2x+32 11 (2x+1) (2x) - x² (2) 2x 4 x² 420 – 2x² (2x+1)2 2x² +22 (2x+12 f'(x) = an(n+1) (2x+1)2