Calculus 1 diffrention

Question

Find the derivative of the function.

arcsinsquaroot(sin(3θ))

Answer 1

y= arcsin( sqrt(sin(3T)))

Derivative is

[ 1 - [sqrt(sin(3T))]^2]^(-1/2) (sin(3T))^(-1/2) 3cos(3T) dT

[ 1 - (sin(3T)) ] ^(-1/2) (sin(3T))^(-1/2) 3 cos(3T) dT

= 3 cos(3T) dt

------------------------------------- =

sqrt[ 1 - (sin(3T))] sqrt(sin(3T))