[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
_
[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