anonymous
  • anonymous
Use the chain rule to find the derivative of (2x-7)^3.
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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chestercat
  • chestercat
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myininaya
  • myininaya
So the chain rule is: |dw:1348707512136:dw|
myininaya
  • myininaya
f(x) is the outside function g(x) is the inside function
mathslover
  • mathslover
Should I interrupt?

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myininaya
  • myininaya
Which function in this problem is f(x)?
myininaya
  • myininaya
Which function in this problem is g(x)?
anonymous
  • anonymous
the power of 3 is the outside function, or f(x) and 2x-7 is the inside function or g(x)
myininaya
  • myininaya
So f(x)=x^3 and g(x)=2x-7 correct :)
mathslover
  • mathslover
how ?
myininaya
  • myininaya
f is the outside function g is the inside 2x-7 is inside the ( )^3
myininaya
  • myininaya
g is inside f
myininaya
  • myininaya
so g is 2x-7 f is x^3
myininaya
  • myininaya
\[f(g(x))=f(2x-7)=(2x-7)^3 \text{ since } f(x)=x^3 \text{ and } g(x)=2x-7\]
myininaya
  • myininaya
Now if you want just plug into the formula above that I gave you
anonymous
  • anonymous
ok so you would set it up x^3(2x-7)^2?
myininaya
  • myininaya
The formula known as the chain rule.
myininaya
  • myininaya
If g(x)=2x-7, then g'(x)= If f(x)=x^3, then f'(x)=?
anonymous
  • anonymous
ohhh 3x^2
myininaya
  • myininaya
And (2x-7)'=?
anonymous
  • anonymous
2
myininaya
  • myininaya
\[(f(g(x))'=f'(g(x))\cdot g'(x)=f'(2x-7) \cdot 2\]
myininaya
  • myininaya
Now to find f'(2x-7) you need to plug 2x-7 into f'
mathslover
  • mathslover
is this the same : f(g(x)) = f(x) g(x)
mathslover
  • mathslover
OK i am interrupting the solution, will take time from @myininaya mam to teach me this,
myininaya
  • myininaya
f(g(x)) means f composed with g
myininaya
  • myininaya
It is not multiplication
anonymous
  • anonymous
would it be 3x^2(2x-7)x2?
myininaya
  • myininaya
No not exactly
anonymous
  • anonymous
does the 2x-7 have an exponent?
myininaya
  • myininaya
f'(x)=3x^2 f'(2x-7)= <---to find this one replace x with 2x-7
anonymous
  • anonymous
why?
myininaya
  • myininaya
the new input is 2x-7
myininaya
  • myininaya
all the outputs have this form 3x^2
myininaya
  • myininaya
except x is the input
myininaya
  • myininaya
and for f'(2x-7), the new input is 2x-7
anonymous
  • anonymous
i don't understand...
anonymous
  • anonymous
|dw:1348708652193:dw|
anonymous
  • anonymous
Tip: Try to sense the pattern in order to absorb the chain rule formula if you're looking for them online
anonymous
  • anonymous
ok so 3(2x-7)^2 x 2?
anonymous
  • anonymous
@Shironlom ?
cgreenwade2000
  • cgreenwade2000
Yes.
anonymous
  • anonymous
thank you!

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