What is the derivative of sqrt(1+sin(2x)) ?

The derivative of sqrt(1+sin(2x)) is (cos(2x))/(sqrt(1+sin(2x)))

What is the first derivative of sqrt(1+sin(2x)) ?

The first derivative of sqrt(1+sin(2x)) is (cos(2x))/(sqrt(1+sin(2x)))

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

\frac{cos ( 2 x )}{1 + sin ( 2 x )}

Solution steps

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

Apply the chain rule:

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

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

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

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

Simplify

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

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

What is the derivative of sqrt(1+sin(2x)) ?
The derivative of sqrt(1+sin(2x)) is (cos(2x))/(sqrt(1+sin(2x)))
What is the first derivative of sqrt(1+sin(2x)) ?
The first derivative of sqrt(1+sin(2x)) is (cos(2x))/(sqrt(1+sin(2x)))