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anonymous
 5 years ago
find the derivative:
(3x+1)^3/(13x)^4
I get the answer (3x+1)^2+(9x+21)/(13x)^5
is this correct?
anonymous
 5 years ago
find the derivative: (3x+1)^3/(13x)^4 I get the answer (3x+1)^2+(9x+21)/(13x)^5 is this correct?

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anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0the + between the 2 equations in the answer should not be there should be (3x+1)^2 (9x+21)/(13x)^5

amistre64
 5 years ago
Best ResponseYou've already chosen the best response.0[ 9 (13x)^4 (3x+1)^2 ]  [ 12 (3x+1)^3 (13x)^3 ]  (13x)^8

amistre64
 5 years ago
Best ResponseYou've already chosen the best response.0just working it out in me head :)

amistre64
 5 years ago
Best ResponseYou've already chosen the best response.09bt'  (12b't) 9bt' + 12b't  =  b^2 b^2 the (+) is good

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0you lost me on that one

amistre64
 5 years ago
Best ResponseYou've already chosen the best response.0we get 2 terms up top that are made up of multiplication. the first term has a (+)9 as a constant, and the 2nd term has a ()12 as a constant. 9 12 = 9+12

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0ok I got that. I guess the way it was written confussed me

amistre64
 5 years ago
Best ResponseYou've already chosen the best response.0probably, I was just trying to clean it up for my eyes :)

amistre64
 5 years ago
Best ResponseYou've already chosen the best response.0for simplicity: r = (13x) ; s = (3x+1) 3 r^3 s^2 (3r + 4s)  r^8

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0Let f(x) and g(x) be the Numerator and the Denominator of the given fraction respectively. The derivative of the fraction in terms of the above functions is:\[\frac{f'[x]}{g[x]}\frac{f[x] g'[x]}{g[x]^2} \] Plug in the function values and their associated derivatives and you should get: \[\frac{9 (1+3 x)^2}{(13 x)^4}+\frac{12 (1+3 x)^3}{(13 x)^5} \]

amistre64
 5 years ago
Best ResponseYou've already chosen the best response.0rob: I dont follow that.....

amistre64
 5 years ago
Best ResponseYou've already chosen the best response.0might be right, but im lost on it :)

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0To start from the beginning. mom wants to know if the derivative of \[{(3x+1)^3 \over {(13x)^4}} \] is equal to: \[(3 x+1)^2+\frac{(9 x+21)}{(13 x)^5} \] The answer is no. The derivative is: \[\frac{9 (1+3 x)^2}{(13 x)^4}+\frac{12 (1+3 x)^3}{(13 x)^5} \] Let \[\frac{(3 x+1)^3}{(13 x)^4}=\frac{f(x)}{g(x)} \] The derivative of f(x)/g(x) is \[\frac{f'(x)}{g(x)}\frac{f(x) g'(x)}{g(x)^2} \] \[f(x) = (1+3x)^3, f'(x) = 9(1+3x)^2 \] \[g(x) = (13x)^4, g'(x) = 12(13x)^3\] Plug in the values for f(x), f'(x), g(x) and g'(x) into the derivative of the f(x)/g(x) and one should end up with the equivalent of the derivative. \[\frac{9 (1+3 x)^2}{(13 x)^4}\frac{(1+3 x)^3 \left(12 (13 x)^3\right)}{\left((13 x)^4\right)^2} \] or \[\frac{9 (1+3 x)^2}{(13 x)^4}+\frac{12 (1+3 x)^3}{(13 x)^5} \]
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