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lizlozada
Group Title
Use the chain rule to find the derivative of (2x7)^3.
 2 years ago
 2 years ago
lizlozada Group Title
Use the chain rule to find the derivative of (2x7)^3.
 2 years ago
 2 years ago

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myininaya Group TitleBest ResponseYou've already chosen the best response.2
So the chain rule is: dw:1348707512136:dw
 2 years ago

myininaya Group TitleBest ResponseYou've already chosen the best response.2
f(x) is the outside function g(x) is the inside function
 2 years ago

mathslover Group TitleBest ResponseYou've already chosen the best response.0
Should I interrupt?
 2 years ago

myininaya Group TitleBest ResponseYou've already chosen the best response.2
Which function in this problem is f(x)?
 2 years ago

myininaya Group TitleBest ResponseYou've already chosen the best response.2
Which function in this problem is g(x)?
 2 years ago

lizlozada Group TitleBest ResponseYou've already chosen the best response.0
the power of 3 is the outside function, or f(x) and 2x7 is the inside function or g(x)
 2 years ago

myininaya Group TitleBest ResponseYou've already chosen the best response.2
So f(x)=x^3 and g(x)=2x7 correct :)
 2 years ago

myininaya Group TitleBest ResponseYou've already chosen the best response.2
f is the outside function g is the inside 2x7 is inside the ( )^3
 2 years ago

myininaya Group TitleBest ResponseYou've already chosen the best response.2
g is inside f
 2 years ago

myininaya Group TitleBest ResponseYou've already chosen the best response.2
so g is 2x7 f is x^3
 2 years ago

myininaya Group TitleBest ResponseYou've already chosen the best response.2
\[f(g(x))=f(2x7)=(2x7)^3 \text{ since } f(x)=x^3 \text{ and } g(x)=2x7\]
 2 years ago

myininaya Group TitleBest ResponseYou've already chosen the best response.2
Now if you want just plug into the formula above that I gave you
 2 years ago

lizlozada Group TitleBest ResponseYou've already chosen the best response.0
ok so you would set it up x^3(2x7)^2?
 2 years ago

myininaya Group TitleBest ResponseYou've already chosen the best response.2
The formula known as the chain rule.
 2 years ago

myininaya Group TitleBest ResponseYou've already chosen the best response.2
If g(x)=2x7, then g'(x)= If f(x)=x^3, then f'(x)=?
 2 years ago

lizlozada Group TitleBest ResponseYou've already chosen the best response.0
ohhh 3x^2
 2 years ago

myininaya Group TitleBest ResponseYou've already chosen the best response.2
And (2x7)'=?
 2 years ago

myininaya Group TitleBest ResponseYou've already chosen the best response.2
\[(f(g(x))'=f'(g(x))\cdot g'(x)=f'(2x7) \cdot 2\]
 2 years ago

myininaya Group TitleBest ResponseYou've already chosen the best response.2
Now to find f'(2x7) you need to plug 2x7 into f'
 2 years ago

mathslover Group TitleBest ResponseYou've already chosen the best response.0
is this the same : f(g(x)) = f(x) g(x)
 2 years ago

mathslover Group TitleBest ResponseYou've already chosen the best response.0
OK i am interrupting the solution, will take time from @myininaya mam to teach me this,
 2 years ago

myininaya Group TitleBest ResponseYou've already chosen the best response.2
f(g(x)) means f composed with g
 2 years ago

myininaya Group TitleBest ResponseYou've already chosen the best response.2
It is not multiplication
 2 years ago

lizlozada Group TitleBest ResponseYou've already chosen the best response.0
would it be 3x^2(2x7)x2?
 2 years ago

myininaya Group TitleBest ResponseYou've already chosen the best response.2
No not exactly
 2 years ago

lizlozada Group TitleBest ResponseYou've already chosen the best response.0
does the 2x7 have an exponent?
 2 years ago

myininaya Group TitleBest ResponseYou've already chosen the best response.2
f'(x)=3x^2 f'(2x7)= <to find this one replace x with 2x7
 2 years ago

myininaya Group TitleBest ResponseYou've already chosen the best response.2
the new input is 2x7
 2 years ago

myininaya Group TitleBest ResponseYou've already chosen the best response.2
all the outputs have this form 3x^2
 2 years ago

myininaya Group TitleBest ResponseYou've already chosen the best response.2
except x is the input
 2 years ago

myininaya Group TitleBest ResponseYou've already chosen the best response.2
and for f'(2x7), the new input is 2x7
 2 years ago

lizlozada Group TitleBest ResponseYou've already chosen the best response.0
i don't understand...
 2 years ago

Shironlom Group TitleBest ResponseYou've already chosen the best response.0
dw:1348708652193:dw
 2 years ago

Shironlom Group TitleBest ResponseYou've already chosen the best response.0
Tip: Try to sense the pattern in order to absorb the chain rule formula if you're looking for them online
 2 years ago

lizlozada Group TitleBest ResponseYou've already chosen the best response.0
ok so 3(2x7)^2 x 2?
 2 years ago

lizlozada Group TitleBest ResponseYou've already chosen the best response.0
@Shironlom ?
 2 years ago

cgreenwade2000 Group TitleBest ResponseYou've already chosen the best response.0
Yes.
 2 years ago

lizlozada Group TitleBest ResponseYou've already chosen the best response.0
thank you!
 2 years ago
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