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bmelyk Group TitleBest ResponseYou've already chosen the best response.1
Use the appropriate rule or combination of rules to find the derivative of the function defined below. \[y=2(\sin(6x)+\cos(x^3))^\frac{ 1 }{ 2 }\]
 one year ago

bmelyk Group TitleBest ResponseYou've already chosen the best response.1
not even sure how to start this one. ;( looks like it would the the chain rule of course.
 one year ago

hartnn Group TitleBest ResponseYou've already chosen the best response.1
first what is derivative of x^{1/2} = ?
 one year ago

hartnn Group TitleBest ResponseYou've already chosen the best response.1
we always go from outer function to inner function
 one year ago

hartnn Group TitleBest ResponseYou've already chosen the best response.1
\(y'=2(1/2)(\sin(6x)+\cos(x^3))^\frac{ 1 }{ 2 }d/dx(\sin(6x)+\cos(x^3))\)
 one year ago

bmelyk Group TitleBest ResponseYou've already chosen the best response.1
options for the right answer are: \[a)2*\frac{ \cos(6x)\sin(x^3) }{ (\sin(6x)+cox(x^3))^1/2 }\] \[b)\frac{ \cos(6x) +\sin(x^3)}{ (\sin(6x)+\cos(x^3))^\frac{ 1 }{ 2 } }\] \[c)\frac{ 12 }{ 6x^\frac{ 1 }{ 2 } }*\cos(6x)\frac{ 6 }{ \cos(x^3)^\frac{ 1 }{ 2 } }*\sin(x^3)*x^2\] \[d)\frac{ 1 }{ (\sin(6x)^\frac{ 1 }{ 2 }+\cos(x^3))^\frac{ 1 }{ 2 } }\] \[e)\frac{ 6*\cos(6x)3x^2*\sin(x^3) }{ (\sin(6x)+\cos(x^3))^\frac{ 1 }{ 2 } }\] f) same as e only 2 outside of the fraction. \[g) \frac{ 2 }{ \sin(6x)+\cos(x^3))^1/2 }\] \[h) \frac{ 6 }{ \sin(6x)^\frac{ 1 }{ 2 } }*\cos6x\frac{ 3 }{ \cos(x^3)^\frac{ 1 }{ 2 } }*\sin(x^3)*x^2\]
 one year ago

hartnn Group TitleBest ResponseYou've already chosen the best response.1
u got my last comment ? how i got that ?
 one year ago

bmelyk Group TitleBest ResponseYou've already chosen the best response.1
and i had that so far.
 one year ago

bmelyk Group TitleBest ResponseYou've already chosen the best response.1
yesi got that.
 one year ago

hartnn Group TitleBest ResponseYou've already chosen the best response.1
so what is d/dx(sin(6x)+cos(x^3)) ?
 one year ago

bmelyk Group TitleBest ResponseYou've already chosen the best response.1
do i use the product rule for sin*6x and cos*x^3?
 one year ago

hartnn Group TitleBest ResponseYou've already chosen the best response.1
there is no product, so NO u can treat them individually also what is d/dx (sin 6x) = ?
 one year ago

hartnn Group TitleBest ResponseYou've already chosen the best response.1
i mean only cos 6x ?
 one year ago

hartnn Group TitleBest ResponseYou've already chosen the best response.1
u need chain rule here too, right ?
 one year ago

hartnn Group TitleBest ResponseYou've already chosen the best response.1
yes! times 6, because u'll have d/dx(6x)
 one year ago

hartnn Group TitleBest ResponseYou've already chosen the best response.1
yup, what about 2nd term ? d/dx (cos (x^3)) = ?
 one year ago

bmelyk Group TitleBest ResponseYou've already chosen the best response.1
sinx^3(3x^2)
 one year ago

hartnn Group TitleBest ResponseYou've already chosen the best response.1
absolutely correct! u got it :)
 one year ago

hartnn Group TitleBest ResponseYou've already chosen the best response.1
so which option is it ?
 one year ago

hartnn Group TitleBest ResponseYou've already chosen the best response.1
put everything together, and u'll get it.
 one year ago

hartnn Group TitleBest ResponseYou've already chosen the best response.1
yes, correct :)
 one year ago

hartnn Group TitleBest ResponseYou've already chosen the best response.1
i hope chain rule is clearer to u now.....
 one year ago
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