A community for students.
Here's the question you clicked on:
 0 viewing
anonymous
 4 years ago
Use the appropriate rule or combination of rules to find the derivative of the function defined below.
y = sin (x^4) cos (x^4)
anonymous
 4 years ago
Use the appropriate rule or combination of rules to find the derivative of the function defined below. y = sin (x^4) cos (x^4)

This Question is Closed

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0i used the product rule for both sin and cos to get (sin*4x^3+x^4*cos)(cos*4x^3*x^4sinx)

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0but my answer should look something like: 4cos(x^4)^2*x^4 4sin(x^4)^2*x^4

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0product rule and chain rule

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0first differentiate sin(x^4) and then x^4.. do the same for cos also

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0the answer you wrote second is not right either you need \((fg)'=f'g+g'f\) with \[f(x)=\sin(x^4), f'(x)=\cos(x^4)\times 4x^3=4x^3\cos(x^4)\]

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0similarly if \(g(x)=\cos(x^4)\) then \(g'(x)=\sin(x^4)\times 4x^3=4x^3\sin(x^4)\)

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0@satellite73 said... there will be no x^4 term it is x^3 term

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0i thought that sin and x^4 were two different factors.

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0should i end up with something that looks like: \[4x^3*\cos(x^4)*\cos(x^4)+(4sinx^3*\sin(x^4))*\sin(x^4)\]

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0ok for simplicity.. do one thing.. let some y = x^4

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0now your equation will be sin(y)cos(y)..

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0so i get: siny'cosy+cosy'siny

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0you know how to differentiate this right.. that will (cos(y)^2sin(y)^2)dy

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0i do the product as: fg'+gf'

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0yes perfect.. d(uv) =vd(u)+ud(v) right.. v =cos(y) u=sin(y).. from this you will get the above thing

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0i don't see how you're getting it to the power of 2 when it should be 11. shouldnt it?

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0now our y = x^4.. so y'= (4x^3) x'

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0put y and y' in above equation.. what do you get.. 4x^3(cos(x^4)^2sin(x^4)^2)

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0i didn't get everything to the power of 2, i just had(sin(4x^3)+cos(x^4))+((cos(4x^3)sin(x^4)

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0what you have seems to look like that answer though is it?

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0ok.. how did you get 4terms?

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0mistake you are would probably be this.. you are combining both product rule and chain rule..

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0i think that is what i'm doing, i thought that is what i neeeded to do. so my answer should be: 4x^3(cos(x^4)^2sin(x^4)^2)

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0see when you differentiate sin(x^4).. first you sin derivative (cos(x^4)*(derivative of x^4))this whole thing is multiplied by cos(x^4).. do the same for cos(x^4) also

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0yes i have that done.

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0is 4x^3(cos(x^4)^2sin(x^4)^2) what i should have? i find it easier to have a correct answer so i can look through my workings and see what i've done wrong.

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0yes.. that is what you should get..

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0can i write it as: 4x^3*cos(x^4)^2sin(x^4)^2
Ask your own question
Sign UpFind more explanations on OpenStudy
Your question is ready. Sign up for free to start getting answers.
spraguer
(Moderator)
5
→ View Detailed Profile
is replying to Can someone tell me what button the professor is hitting...
23
 Teamwork 19 Teammate
 Problem Solving 19 Hero
 Engagement 19 Mad Hatter
 You have blocked this person.
 ✔ You're a fan Checking fan status...
Thanks for being so helpful in mathematics. If you are getting quality help, make sure you spread the word about OpenStudy.