What is the d/(dθ)(sqrt(1+sin(2θ))) ?

The d/(dθ)(sqrt(1+sin(2θ))) is (cos(2θ))/(sqrt(1+sin(2θ)))

What is the first d/(dθ)(sqrt(1+sin(2θ))) ?

The first d/(dθ)(sqrt(1+sin(2θ))) is (cos(2θ))/(sqrt(1+sin(2θ)))

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\frac{d}{d θ} (1 + sin (2 θ))

\frac{cos ( 2 θ )}{1 + sin ( 2 θ )}

Solution steps

\frac{d}{d θ} (1 + sin (2 θ))

Apply the chain rule:

\frac{1}{2 1 + sin ( 2 θ )} \frac{d}{d θ} (1 + sin (2 θ))

= \frac{1}{2 1 + sin ( 2 θ )} \frac{d}{d θ} (1 + sin (2 θ))

\frac{d}{d θ} (1 + sin (2 θ)) = 2 cos (2 θ)

= \frac{1}{2 1 + sin ( 2 θ )} \cdot 2 cos (2 θ)

Simplify

\frac{1}{2 1 + sin ( 2 θ )} \cdot 2 cos (2 θ) : \frac{cos ( 2 θ )}{1 + sin ( 2 θ )}

= \frac{cos ( 2 θ )}{1 + sin ( 2 θ )}

What is the d/(dθ)(sqrt(1+sin(2θ))) ?
The d/(dθ)(sqrt(1+sin(2θ))) is (cos(2θ))/(sqrt(1+sin(2θ)))
What is the first d/(dθ)(sqrt(1+sin(2θ))) ?
The first d/(dθ)(sqrt(1+sin(2θ))) is (cos(2θ))/(sqrt(1+sin(2θ)))