Question

differentiate

y= sin^4 root(u)

*More interested in the "how to"*

Answer 1

use the chain rule:
(sin(sqrt(u))^4

"outside" function is ( )^4 -> 4*( )^3
"inside" function is sin(sqrt(u)) -> cos(sqrt(u))
still have another
'inside' function though so (sqrt(u)) ' = 1/2*u^(-1/2)

4(sin(sqrt(u))^3 * cos(sqrt(u)) * 1/2*u^(-1/2)

Answer 2

thanks! i keep forgetting that sin^4x is the same as sinx^4, silly me.