Question

could you solve this for me please? y=(x^2-5x+8)^6.

can i expand through with the exponent 6?? how do i solve this.

Answer 1

you wanto differentiate it ?

Answer 2

if so, use chain rule

Answer 3

yeah

Answer 4

show me please

Answer 5

Do you know the Chain Rule?

Answer 6

yeah...but dis looks soo confusing

Answer 7

OK. Let's see:

The first function we see is x^2 - 5x + 8.
The second function that is acting on the first function is (...)^6.

Answer 8

ok

Answer 9

Recall the formula for the Chain Rule.\[\dfrac{d}{dx}f(g(x)) = f'(g(x)) \times g'(x)\]

Answer 10

So what is \(f'(g(x))\)?

Answer 11

Hmm, do you have any thoughts so far? Are you able to follow?

Answer 12

\[f(g(x))\]The \(g\) is the "inside" function and the \(f\) is another function which is "outside" the inside function.

Answer 13

ok

Answer 14

So here, the \(g\) is \(x^2 - 5x + 8\) because it's the "inside" function.
The second function \(f\) is the "something to the power six" function because it's acting on the inside function.

Answer 15

f′(g(x))=6(2x-5)^5

Answer 16

Hmm, you leave the \(x^2 - 5x + 8\) in that as it is. You're only differentiating the outside function.

Answer 17

okay

Answer 18

\[f'(g(x)) = 6(x^2 - 5x + 8)^5 \]\[g'(x) = 2x - 5\]

Answer 19

so d/dxf(g(x))=f′(g(x))×g′(x)
==6(x^2-5x+8)^5 * (2x-5)

Answer 20

thanks a loads