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Use the chain rule to find the derivative of (2x-7)^3.

Mathematics
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So the chain rule is: |dw:1348707512136:dw|
f(x) is the outside function g(x) is the inside function
Should I interrupt?

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Other answers:

Which function in this problem is f(x)?
Which function in this problem is g(x)?
the power of 3 is the outside function, or f(x) and 2x-7 is the inside function or g(x)
So f(x)=x^3 and g(x)=2x-7 correct :)
how ?
f is the outside function g is the inside 2x-7 is inside the ( )^3
g is inside f
so g is 2x-7 f is x^3
\[f(g(x))=f(2x-7)=(2x-7)^3 \text{ since } f(x)=x^3 \text{ and } g(x)=2x-7\]
Now if you want just plug into the formula above that I gave you
ok so you would set it up x^3(2x-7)^2?
The formula known as the chain rule.
If g(x)=2x-7, then g'(x)= If f(x)=x^3, then f'(x)=?
ohhh 3x^2
And (2x-7)'=?
2
\[(f(g(x))'=f'(g(x))\cdot g'(x)=f'(2x-7) \cdot 2\]
Now to find f'(2x-7) you need to plug 2x-7 into f'
is this the same : f(g(x)) = f(x) g(x)
OK i am interrupting the solution, will take time from @myininaya mam to teach me this,
f(g(x)) means f composed with g
It is not multiplication
would it be 3x^2(2x-7)x2?
No not exactly
does the 2x-7 have an exponent?
f'(x)=3x^2 f'(2x-7)= <---to find this one replace x with 2x-7
why?
the new input is 2x-7
all the outputs have this form 3x^2
except x is the input
and for f'(2x-7), the new input is 2x-7
i don't understand...
|dw:1348708652193:dw|
Tip: Try to sense the pattern in order to absorb the chain rule formula if you're looking for them online
ok so 3(2x-7)^2 x 2?
Yes.
thank you!

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