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 2 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)
 2 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)

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bmelyk
 2 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)

bmelyk
 2 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

satellite73
 2 years ago
Best ResponseYou've already chosen the best response.1product rule and chain rule

theloser
 2 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

satellite73
 2 years ago
Best ResponseYou've already chosen the best response.1the answer you wrote second is not right either you need \((fg)'=f'g+g'f\) with \[f(x)=\sin(x^4), f'(x)=\cos(x^4)\times 4x^3=4x^3\cos(x^4)\]

satellite73
 2 years ago
Best ResponseYou've already chosen the best response.1similarly if \(g(x)=\cos(x^4)\) then \(g'(x)=\sin(x^4)\times 4x^3=4x^3\sin(x^4)\)

theloser
 2 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

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

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

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

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

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

theloser
 2 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

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

theloser
 2 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

bmelyk
 2 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?

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

theloser
 2 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)

bmelyk
 2 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)

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

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

theloser
 2 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..

bmelyk
 2 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)

theloser
 2 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

bmelyk
 2 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.

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

bmelyk
 2 years ago
Best ResponseYou've already chosen the best response.0can i write it as: 4x^3*cos(x^4)^2sin(x^4)^2
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