find derivative of 1) cos(x ln x), 2) sin(sin(sin x))?

Question

dy/dx of sin(sin x) is cos(sin x)*cos x, but what then? and i'm really not sure about the ln question...

Answer 1

Use the chain rule.

1) d[cos(x lnx)/dx = sin(x lnx)*[lnx + x/x] = (1 + lnx)[sin(x lnx)]

2) d[sin(sin(sin x))]/dx = cos(sin(sin x))[cos(sin x)(cos x)]

Answer 2

1)

d(cos(x ln x)) =

-sin (x ln x)[x/x + lnx (1) ]

-(1 + ln x) sinx ( x ln x)

2)

sin(sin (sinx)

differentiate

[cos(sin(sinx)][(cos(sinx)] (cosx)