Question

if f(x)= (2x+1)^4 than what is the fourth derivative?

Answer 1

take the first
then the second,
then the third
then the fourth
NO shortcut.
kha kha

Answer 2

can you explain how to do the first one, I think i am messing up the chain rule part

Answer 3

(2x+1)^4 the first derivative = 4((2x+1)^3* 2

Answer 4

=8(2x+1)^3

Answer 5

so the second derivative would then be 48(2x+1)^2 ?

Answer 6

yup

Answer 7

and nothing on the inside changes?

Answer 8

yup, fortunately, the inside term is just degree of 1. if its degree is 5, you are gonna go crazy khakhakha

Answer 9

so when you go from the 3rd derivative to the 4th derivative: f^iii(x)= 192(2x+1) to f^iv(x)=384(2x+1)... is that right?

Answer 10

nope, the 3rd is ok, but the 4th is not

Answer 11

so what happens with the parenthesis?

Answer 12

Actually, it is
I am sorry, I must go back and explain you why
\[(2x+1)^4)'= 4(2x+1)^3*\color{red}{(2x+1)'}\]
and \(\color{red}{(2x+1)'}=2\)
that's why the first derivative =\( 8 (2x+1)^3\)

Answer 13

now, the second derivative
\[(8(2x+1)^3)'=8*3(2x+1)^2*\color{red}{(2x+1)'}\]
again, it is =2, so that the second derivative = \(48(2x+1)^2\)

Answer 14

so then is the 4th derivative just a number and you just use the derivative of (2x+1), or 2?

Answer 15

the third one = 192(2x+1)= 394x + 394
so the fourth one is just 394, no more x

Answer 16

ah, you factor it out and then take the derivative. I understand now. Thank you

Answer 17

ok