Derivative Question, please help

[rainforme]

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Can someone explain to me how did Dr. Collins got -12 for this question? Thanks.

17-9 If f(x) = (2x+1)^6, then f(-1) =

I did it this way.

f(x) = x^6
g(x) = 2x +1
f'(x) = 6x^5
g'(x) = 2

then i plugged it in the formula f'(g(x)) g'x)
6x^5(2x+1)(2)
which equals to (12x^6 + 6x^5)2

24x^6 +12x^5
24(-1)^6 + 12(-1)^5
24 + -12 = 12

please let me know where I was wrong. Thanks so much....

 

[Lubeckd]

have you used Chain rule in calculus? did you take a class in it?
If f(x) = (2x+1)^6, then f(-1) =

F (-1) = Part 1 of the chain rule, bring the 6 down, and subtract 1.
6(2x+1)^5

Part 2 you find the Derivative of the the inside.
which is this (2x+1)
To get 2.

Part 3
6(2x+1)^5 x 2
2x6= 12
Substitute the -1 for x
12 (2(-1)+1)
(-1)(12) = -12

 

[amox]

have you used Chain rule in calculus? did you take a class in it?
If f(x) = (2x+1)^6, then f(-1) =

F (-1) = Part 1 of the chain rule, bring the 6 down, and subtract 1.
6(2x+1)^5

Part 2 you find the Derivative of the the inside.
which is this (2x+1)
To get 2.

Part 3
6(2x+1)^5 x 2
2x6= 12
Substitute the -1 for x
12 (2(-1)+1)
(-1)(12) = -12

This is correct.

I took Calc 1-3 and remember this was used in Calc 1-2 quite frequently.

Here is another example.

Take the derivative of (4x+19)^2

First bring the exponent down as a coefficient, and -1 from the exponent.

2(4x+19)^1

Now multiply by the derivative of the inside of the parenthesis. (4x+19)d/dx = 4

2(4x+19)*(4)

Simplify

8(4x+19)

And if its defined at f(-1).

8(4(-1)+19)

8(-4+19)

8(15)

120