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

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

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

hartnn
 2 years ago
Best ResponseYou've already chosen the best response.1we always go from outer function to inner function

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

bmelyk
 2 years ago
Best ResponseYou've already chosen the best response.1options 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. \[g) \frac{ 2 }{ \sin(6x)+\cos(x^3))^1/2 }\] \[h) \frac{ 6 }{ \sin(6x)^\frac{ 1 }{ 2 } }*\cos6x\frac{ 3 }{ \cos(x^3)^\frac{ 1 }{ 2 } }*\sin(x^3)*x^2\]

hartnn
 2 years ago
Best ResponseYou've already chosen the best response.1u got my last comment ? how i got that ?

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

bmelyk
 2 years ago
Best ResponseYou've already chosen the best response.1do i use the product rule for sin*6x and cos*x^3?

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

hartnn
 2 years ago
Best ResponseYou've already chosen the best response.1u need chain rule here too, right ?

hartnn
 2 years ago
Best ResponseYou've already chosen the best response.1yes! times 6, because u'll have d/dx(6x)

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

hartnn
 2 years ago
Best ResponseYou've already chosen the best response.1absolutely correct! u got it :)

hartnn
 2 years ago
Best ResponseYou've already chosen the best response.1put everything together, and u'll get it.

hartnn
 2 years ago
Best ResponseYou've already chosen the best response.1i hope chain rule is clearer to u now.....
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