[derivatives - rational exponents][section 8]

(1.)  f(x) = x2/5 + 2x1/3

f'(x) = (2/5)x-3/5 + (2/3)x-2/3   use the power rule

(2.)  f(x) = 5x-2/9

f'(x) = (-10/9)x-11/9      use the power rule

(3.)  f(x) = (x2 + 1)5/3

f'(x) = (10x/3)(x2 + 1)2/3   use the chain rule

(4.)  f(x) = (x2 - 1)-2/3

f'(x) = (-4x/3)(x2 - 1)-5/3   use the chain rule

(5.)  f(x) = (x3 + 3)1/10

f'(x) = (3x2/10)(x3 + 3)-9/10    use the chain rule

(6.)  f(x) = (x5 + 2x + 1)3/2

f'(x) = (3/2)(5x4 + 2)(x5 + 2x + 1)1/2  use the chain rule

(7.)  s(t) = (t10 - 2)4/7

s'(t) = (4/7)(10t9)(t10 - 2)-3/7    use the chain rule

(8.)  s(t) = (t3 + t2 + 1)5/8

s'(t) = (5/8)(3t2 + 2t)(t3 + t2 + 1)-3/8   use the chain rule
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(9.)  g(u) = \3/u3 + 3u + 1

g(u) = (u3 + 3u + 1)1/3     write using the 1/3 power

g'(u) = (1/3)(3u2 + 3)(u3 + 3u + 1)-2/3  use the chain rule

g'(u) = (u2 + 1)(u3 + 3u + 1)-2/3    multiply thru

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(10.)  s(t) = (t2 + 1)
3
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s'(t) = (2t√3)(t2 + 1)(√3 - 1)       use the chain rule