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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

lizlozada
 3 years ago
Best ResponseYou've already chosen the best response.0i don't understand...

Shironlom
 3 years ago
Best ResponseYou've already chosen the best response.0dw:1348708652193:dw

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