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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?

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)'=?

\[(f(g(x))'=f'(g(x))\cdot g'(x)=f'(2x-7) \cdot 2\]

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|

ok so 3(2x-7)^2 x 2?

Yes.

thank you!