Question

need someone to walk me through this question, please:

Answer 1

Use the appropriate rule or combination of rules to find the derivative of the function defined below.
\[y=2(\sin(6x)+\cos(x^3))^\frac{ 1 }{ 2 }\]

Answer 2

not even sure how to start this one. ;(
looks like it would the the chain rule of course.

Answer 3

first what is derivative of x^{1/2} = ?

Answer 4

1/2x^-1/2

Answer 5

we always go from outer function to inner function

Answer 6

\(y'=2(1/2)(\sin(6x)+\cos(x^3))^\frac{ -1 }{ 2 }d/dx(\sin(6x)+\cos(x^3))\)

Answer 7

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.

\[g) \frac{ 2 }{ \sin(6x)+\cos(x^3))^1/2 }\]

\[h) \frac{ 6 }{ \sin(6x)^\frac{ 1 }{ 2 } }*\cos6x-\frac{ 3 }{ \cos(x^3)^\frac{ 1 }{ 2 } }*\sin(x^3)*x^2\]

Answer 8

u got my last comment ? how i got that ?

Answer 9

and i had that so far.

Answer 10

yesi got that.

Answer 11

so what is d/dx(sin(6x)+cos(x^3)) ?

Answer 12

do i use the product rule for sin*6x and cos*x^3?

Answer 13

there is no product, so NO
u can treat them individually also
what is d/dx (sin 6x) = ?

Answer 14

cos6x

Answer 15

-sinx^3

Answer 16

only ?

Answer 17

i mean only cos 6x ?

Answer 18

times 6?

Answer 19

u need chain rule here too, right ?

Answer 20

yes! times 6, because u'll have d/dx(6x)

Answer 21

cox6x*6

Answer 22

cos6x*6

Answer 23

????

Answer 24

yup, what about 2nd term ?
d/dx (cos (x^3)) = ?

Answer 25

-sinx^3(3x^2)

Answer 26

absolutely correct!
u got it :)

Answer 27

so which option is it ?

Answer 28

e??

Answer 29

put everything together, and u'll get it.

Answer 30

yes, correct :)

Answer 31

awesome!

Answer 32

i hope chain rule is clearer to u now.....