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

1. myininaya

So the chain rule is: |dw:1348707512136:dw|

2. myininaya

f(x) is the outside function g(x) is the inside function

3. mathslover

Should I interrupt?

4. myininaya

Which function in this problem is f(x)?

5. myininaya

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)

7. myininaya

So f(x)=x^3 and g(x)=2x-7 correct :)

8. mathslover

how ?

9. myininaya

f is the outside function g is the inside 2x-7 is inside the ( )^3

10. myininaya

g is inside f

11. myininaya

so g is 2x-7 f is x^3

12. myininaya

$f(g(x))=f(2x-7)=(2x-7)^3 \text{ since } f(x)=x^3 \text{ and } g(x)=2x-7$

13. myininaya

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?

15. myininaya

The formula known as the chain rule.

16. myininaya

If g(x)=2x-7, then g'(x)= If f(x)=x^3, then f'(x)=?

ohhh 3x^2

18. myininaya

And (2x-7)'=?

2

20. myininaya

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

21. myininaya

Now to find f'(2x-7) you need to plug 2x-7 into f'

22. mathslover

is this the same : f(g(x)) = f(x) g(x)

23. mathslover

OK i am interrupting the solution, will take time from @myininaya mam to teach me this,

24. myininaya

f(g(x)) means f composed with g

25. myininaya

It is not multiplication

would it be 3x^2(2x-7)x2?

27. myininaya

No not exactly

does the 2x-7 have an exponent?

29. myininaya

f'(x)=3x^2 f'(2x-7)= <---to find this one replace x with 2x-7

why?

31. myininaya

the new input is 2x-7

32. myininaya

all the outputs have this form 3x^2

33. myininaya

except x is the input

34. myininaya

and for f'(2x-7), the new input is 2x-7

i don't understand...

36. Shironlom

|dw:1348708652193:dw|

37. Shironlom

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?

@Shironlom ?

Yes.