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bmelyk
Group Title
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
 2 years ago
bmelyk Group Title
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
 2 years ago

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

theloser Group TitleBest ResponseYou've already chosen the best response.0
mistake you are would probably be this.. you are combining both product rule and chain rule..
 2 years ago

bmelyk Group TitleBest ResponseYou've already chosen the best response.0
i 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)
 2 years ago

theloser Group TitleBest ResponseYou've already chosen the best response.0
see 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
 2 years ago

bmelyk Group TitleBest ResponseYou've already chosen the best response.0
yes i have that done.
 2 years ago

bmelyk Group TitleBest ResponseYou've already chosen the best response.0
is 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.
 2 years ago

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

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