Question

find the second derivation :

y=(x^3 - 7x + 1)^4

Answer 1

Where are you stuck?

Answer 2

first order derivative is 4(x^3-7x+1)^3 (3x^2-7)

Answer 3

now using multipplication rule again differentiate it wrt x !

Answer 4

there are two ways to solve this.
first, you can expand then do a normal power rule on each term
the other method is to use chain rule

Answer 5

once you've done one of the two ways, you can just go ahead and obtain the second derivative

Answer 6

\[\huge y=(x^3 - 7x + 1)^4\]
\[\huge y'=4(x^3 - 7x + 1)^3 (3x^2 -7)\]
\[ y''=4(x^3 - 7x + 1)^3 (6x)+4(3x^2 -7)3(3x^2 - 7 + 1)^2 (6x)\]
Now simplify it

Answer 7

then the second derivative is =
3*4(x^3-7x+1)^2(3x^2-7)(3x^2-7)+4(x^3-7x+1)(6x)

Answer 8

thanks a lot for all :)

Answer 9

y′′=4(x3−7x+1)3(6x)+4(3x2−7)3(3x2−7+1)2(6x)

I think this it's wrong :(

Answer 10

ya it is ! why multiplying 3 in the first term
?
I think the correct ans =3*4(x^3-7x+1)^2(3x^2-7)(3x^2-7)+4(x^3-7x+1)(6x)

Answer 11

12(x^3-7x+1)^2(3x^2-7)+4(x^3-7x+1)^3(6x)

this is correct ?

Answer 12

12(x^3-7x+1)^2(3x^2-7)(3x^2-7)+4(x^3-7x+1)^3(6x)

sorry I mean this .. ?

Answer 13

ohh yea

Answer 14

thanks @moli1993 :)

Answer 15

np, :)