Find Derivative of y=sin(cos(sinx))

[ggcheck]

Homework Statement

find the derivative using the appropriate rules

y=sin(cos(sinx))

The Attempt at a Solution

d/dx[sin(cos(sinx))] = [cos(cos(sinx))] * [-sin(sinx)] =

-cos(cos(sinx))(sin(sinx))

Is that right?

It doesn't feel right.

 

[rock.freak667]

Try making an extended chain rule...let t=sinx and then u=cost ...and then differentiate and use the chain rule

 

[rocomath]

you're very close! 1 more angle

 

[ggcheck]

is the first factor done? and -sin(sinx) needs more?

 

[ggcheck]

something like this: y= sinu ; u=cos(t) ; t=sinx

d/du[y] * d/dt * d/dx[t] ?

 

[ggcheck]

= cosu * (-sint) * cosx =

-sin(sinx)*cos(cos(sinx))*cosx ??

 

[rock.freak667]

well the chain rule is correct...so I would assume that it is correct

 

[ggcheck]

It wouldn't be uncommon for me to apply a rule incorrectly.

 

[rock.freak667]

Well it is correct