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anonymous
 4 years ago
Let y =(root5(x^8+5)).
Find values A and B so that (dy)/(dx) = A(x^8+5)^B(C x^D)
anonymous
 4 years ago
Let y =(root5(x^8+5)). Find values A and B so that (dy)/(dx) = A(x^8+5)^B(C x^D)

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myininaya
 4 years ago
Best ResponseYou've already chosen the best response.1\[y=\sqrt[5]{x^8+5}\] \[y=(x^8+5)^\frac{1}{5}\] Use the chain rule to find y'

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0what if I need to find A,B,C, and D? what do I plug in?

myininaya
 4 years ago
Best ResponseYou've already chosen the best response.1You need to find y' first to find A,B,C,and D

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0I havent learned the chain rule yet

myininaya
 4 years ago
Best ResponseYou've already chosen the best response.1\[[f(g(x))]'=f'(g(x)) \cdot g'(x) \text{ chain rule }\]

myininaya
 4 years ago
Best ResponseYou've already chosen the best response.1Well you need the chain rule to do this problem.

myininaya
 4 years ago
Best ResponseYou've already chosen the best response.1what is g(x) and what is f(x) if \[f(g(x))=(x^8+5)^\frac{1}{5}\]

myininaya
 4 years ago
Best ResponseYou've already chosen the best response.1No g(x) is the inside function and f(x) is the outside function

myininaya
 4 years ago
Best ResponseYou've already chosen the best response.1\[g(x)=x^8+5 ; f(x)=x^\frac{1}{5}\] \[g'(x)=8x^7+0 ; f(x)=\frac{1}{5}x^{\frac{1}{5}1}=\frac{1}{5}x^\frac{4}{5}\]

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0so I plug this in in the equation now

myininaya
 4 years ago
Best ResponseYou've already chosen the best response.1this one \[y'=[f(g(x))]'=f'(g(x)) \cdot g'(x) \text{ chain rule } \] yes

myininaya
 4 years ago
Best ResponseYou've already chosen the best response.1\[y'=f'(x^8+5) \cdot 8x^7\]

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0now just multiply, right?

myininaya
 4 years ago
Best ResponseYou've already chosen the best response.1you need to plug x^8+5 into f'

myininaya
 4 years ago
Best ResponseYou've already chosen the best response.1\[g'(x)=8x^7+0 ; f'(x)=\frac{1}{5}x^{\frac{1}{5}1}=\frac{1}{5}x^\frac{4}{5}\]

myininaya
 4 years ago
Best ResponseYou've already chosen the best response.1f' is that second one I wrote down just now

myininaya
 4 years ago
Best ResponseYou've already chosen the best response.1\[y'=f'(x^8+5) \cdot 8x^7=\frac{1}{5}(x^8+5)^\frac{4}{5} \cdot 8x^7\]

myininaya
 4 years ago
Best ResponseYou've already chosen the best response.1now you should be able to put it in the form above to get your A,B,C, and D

myininaya
 4 years ago
Best ResponseYou've already chosen the best response.1actually it is already in that form

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0so just look for the A,B,C,D then right?
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