Posted by Alex on Thursday, May 22, 2008 at 8:09pm.
Can anyone explain how to use the chain rule and power rule together to find the first derivative and please do these examples.
f(x) = 3x^4/(sqrt(4x8))
g(x) = ((2x+5)/(6x^2)^4
g(x) = (8x^3)(4x^2+2x3)^5
y = [1/(4x+x^2)^3]^3
Thank you so much!

Calculus  Reiny, Thursday, May 22, 2008 at 10:09pm
I will give you the 'firstline' derivatives of the first two questions
a) f'(x) = [(4x8)^(1/2)(12x^3)  (3x^4)(1/2(4x8)^(1/2)(4)]/(4x8)
= ....
b) I see you had a double bracket at the front, but one bracket is not closed.
Did you mean [(2x+5)/(6x^2)]^4 ?
c) g(x) = (8x^3)(4x^2+2x3)^5
g'(x) = 5(4x^2+2x3)^5(8x+2)(8x^3) + 24x^2(4x^2+2x3)^5
= ....
d) y = [1/(4x+x^2)^3]^3
y = (4x+x^2)^9
y' = 9(4x + x^2)^10(4+2x)
= ....
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