Question

find the 2nd Derivative

y= 7x* sin(x^2)

I tried to do it many times but i got my answer wrong but i dont know why ???

Answer 1

Can you show your work so far? Should be pretty simple application of the product and chain rules.

Answer 2

yeah i know i did the same and i got -2cosx^2-4x^2sinx

Answer 3

How did you get that? You have f(x)=7x, g(x)=sin(x^2), product rule says you do f'(x)g(x)+g'(x)f(x).

Answer 4

So we have f(x)=7x, g(x)=sin(x^2), f'(x)=7, g'(x)=2x cos(x^2), then just plug everything in.

Answer 5

can you show me please so I can know what is my mistake ?

Answer 6

What part haven't I already shown you? I've already broken it down into f(x) and g(x), and already calculated the derivatives of them, literally the only thing remaining to do is plug it back into the product rule formula.

Answer 7

actually the 2nd derivative too not just the first one ?

Answer 8

i found the first one now . 14x^2cosx^2+7sinx^2

Answer 9

Okay, yes, that is correct for the first derivative. Now do the second derivative, again using the product and chain rules.

Answer 10

second derivative is -28x^4sinx^2+14xcosx^2

is that right ?

Answer 11

No, that is not correct. How did you get that, can you show your work?

Answer 12

the correct answer is 42x cosx^2 -28x^3 sinx^2

im really confused with this problem i started doing it right but it turned at the end wrong ?

Answer 13

Yes, I know that is the correct answer. You got the 14xcosx^2 part right, but you got the other part wrong. The product rule part. Can you show your work?

Answer 14

-14x^2cosx^2*2x+7cos(x^2)*2x
and i end with that answer

Answer 15

Okay, no, that's not right at all. First step: split the product into f(x) and g(x). What are they?

Answer 16

Remember the product rule? \[
(fg)'(x)=f'(x)g(x)+f(x)g'(x)
\]

Answer 17

i know what do you mean but i get anther problem and im working on it

y= 4x sinx^2
f(x) 4x f'(x)= 4
g(x)= sinx^2 g'(x)= 2x cos(x^2)

y'= 6x^2cosx^2+4sin x^2

Answer 18

You mean 8, not 6, on that first term of y'

Answer 19

yeah i missed it

Answer 20

im doing now the second derivative

Answer 21

i got -16x^3 sinx^2+8x cos x^2

can you check it ?

Answer 22

You need to use the product rule to differentiate 6x^2cosx^2

Answer 23

you mean 8x^2 cos x^2

i used product rule

Answer 24

Yes, sorry, was copying what you had. You're missing a term. You got the fg' term but not the f'g term

Answer 25

\[f'(x) = 7 \sin \left(x^2\right)+14 x^2
\cos \left(x^2\right)\\

f''(x)= 42 x \cos \left(x^2\right)-28
x^3 \sin \left(x^2\right)
\]

Answer 26

can you show me how did get the f"" ?

Answer 27

I leave the details for you.

Answer 28

but still your answer is wrong ? thats what the web homework said

Answer 29

\[f'(x) = 7 \sin \left(x^2\right)+14 x^2
\cos \left(x^2\right)\\

f''(x) = 14 x \cos(x^2) + 28 x\cos(x^2) - 28 x^3 \sin(x^2)=\\42x\cos(x^2) - 28 x^3 \sin(x^2)
\]

Answer 30

Do you follow me?

Answer 31

yeah but i dont know why it showed me wrong

Answer 32

What did you get as an answer?

Answer 33

24xcosx^2-16x^3sinx^2
this is what showed me

Answer 34

3x cos(x^2) new one

Answer 35

For a new question you should close the question and open a new one.

Answer 36

It is not right
http://www.wolframalpha.com/input/?i=derivative+7+x+sin%28x^2%29
http://www.wolframalpha.com/input/?i=derivative+14+x^2+Cos [x^2]+%2B+7+Sin[x^2]

Answer 37

For the second link, copy and paste in your browser

Answer 38

ok thanks