Question

find the derivative f(θ) = sqrt(sin 2θ )

Answer 1

i'll substitute theta from x, so that it's easy for me to write
theta=x

Answer 2

\(\bf f(\theta)=\sqrt{{\color{blue}{ sin(2\theta)}}}\implies f(\theta)=\sqrt{{\color{blue}{ 2sin(\theta)cos(\theta)}}}\)

chain-rule it
use the product rule for the inner function

Answer 3

f'(x)= (1/2)*(sin2x)^(-1/2)*d(sin2x)/dx

Answer 4

f'(x)= (1/2)*(sin2x)^(-1/2)*2*cos2x

Answer 5

To my knowledge we don't need to use chain rule or simplification of sin2x. That is unnecessary. Correct me if I'm wrong

Answer 6

you're right... you can do away with just the angle as it's, and also use the power rule with the 1/2

Answer 7

yes that is correct thank you for the help!