Differentiate y= sin(4x)?

*Chain Rule*

1. first differentiate the "4x"
then "replace" the 4x with... lets say "u"

so it's sin(u)

2. now differentiate sin(u)

which is cos(u) , replace the u with the "original" which is 4x

so final answer is: 4cos(4x)

dy/dx = 4 cos (4x)

y = sin(4x)

dy/dx = cos(4x) d/dx (4x)
dy/dx = cos 4x (4)
dy/dx = 4 cos(4x)

y = sin(4x)

dy/dx
= d/dx sin(4x)
= cos(4x) d/dx 4x
= cos(4x) * 4
= 4cos(4x)