[the chain rule][section 7]

(1.)  f(x) = (x + 1)3             here is the problem

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

(2.)  f(x) = (x2 - 1)2            here is the problem

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

(3.)  f(x) =(1 + x6)6          here is the problem

f'(x) = 36x5(1 + x6)5    use the chain rule

(4.)   f(x) = (x2 - 4x + 1)5

f'(x) =  5(2x - 4)(x2 - 4x + 1)4   use the chain rule

f'(x) = (10x - 20)(x2 - 4x + 1)4    multiply thru

(5.)  f(x) = (x2 - x3)4           here is the problem

f'(x) =  4(2x - 3x2)(x2 - x3)3  use the chain rule

(6.)  f(x) = (1 - x + x2 - x3)2   here is the problem

f'(x) = 2(-1 + 2x - 3x2)(1 - x + x2 - x3)

[use the chain rule]

(7.)  f(x) = (1 - x2 + x5)3       here is the problem

f'(x) = 3(5x4 - 2x)(1 - x2 + x5)2  use the chain rule
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(8.)  f(x) = (√x + 2)4         here is the problem
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[use (1/2)x-1/2 for the derivative of √x ]
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f'(x) = 2x-1/2(
x + 2)3    use the chain rule
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(9.)  f(x) = (√x - x)3              here is the problem
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f'(x) =  3[(1/2)x-1/2 - 1](
x - x)2 use the chain rule

(10.)  h(y) = (y2 + 3)-4               here is the problem

h'(y) = -8y(y2 + 3)-5     use the chain rule