Please Help (differentiation)

[mathlete1]

i have two questions i really need help on..

Differentiate:
1) y=e^(lncos7x)

2) y= cos(sin(x))

All help is much appreciated
thanks!

[TBeck]

are you familiar with the chain rule? All you need is the chain rule.

[Glaysher]

1) y = e^{ln cos 3x} = cos 3x

[TBeck]

Yes 1 can be simplified and so the derivative of cos7x = -7sin7x

without simplifying it would look like:
dy/dx = d e^(lncos7x)/d lncos7x * d lncos7x/dcos7x * dcos7x/d7x * d7x/dx

= e^(lncos7x) * 1/cos7x * -sin7x * 7

which simplifies to

= cos7x * 1/cos7x * -7sin7x
= -7sin7x

2) y= cos(sin(x))

dy/dx = d cos(sin(x))/d sin(x) * d sin(x)/ dx

= -sin(sin(x)) * cos(x)