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Home Q & A Board Science-Related Homework Help Mathematics
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BUGG123 BUGG123
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Posts: 117
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12 years ago
f(x) = (7-4x)^2

Could someone show the step by step on this problem for me, using the function f(x) above.  I am struggling to understand both these rules.
I apoologize,  I should have said chain  rule instead of product rule.  I need to use both the chain and the genral power rules individually.
I take that back I had it right the first time - general power and product.  Sorry....I thought I typed it wrong.
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wrote...
#1
12 years ago
Use the chain rule:

dy/dx = dy/du * du/dx

u = 7-4x
du/dx= -4
y = u^2
dy/du = 2u  = 2(7-4x) = 14-8x

So when you combine these, you are going to get (-4)(14-8x) = 32x-56
wrote...
#2
12 years ago
f (u) = u²

f '(u) = 2udu

f (x) = (7 - 4x)²

u = (7 - 4x), du = - 4

f '(x) = 2(7 - 4x)(- 4) = - 8(7 - 4x) = - 56 + 32x
wrote...
#3
12 years ago
First , you should apply chain rule .
you may treat (7-4x) as u .
so when u differentiate u^2 =2u=2(7-4x ) (power rule )

then u need to  differentiate (7-4x) =-4
(differentiate 7 a constant =0 ) (differentiate -4x=-4 )
So the ans is 2(7-4x )(-4) =32x-56
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