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

The derivative of sin(sqrt(2x)) is (cos(sqrt(2)sqrt(x)))/(sqrt(2)\sqrt{x)}

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

The first derivative of sin(sqrt(2x)) is (cos(sqrt(2)sqrt(x)))/(sqrt(2)\sqrt{x)}

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

\frac{cos ( 2 x )}{2 x}

Solution steps

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

Simplify

sin (2 x) : sin (2 x)

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

Apply the chain rule:

cos (2 x) \frac{d}{d x} (2 x)

= cos (2 x) \frac{d}{d x} (2 x)

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

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

Simplify

cos (2 x) \frac{1}{2 x} : \frac{cos ( 2 x )}{2 x}

= \frac{cos ( 2 x )}{2 x}

What is the derivative of sin(sqrt(2x)) ?
The derivative of sin(sqrt(2x)) is (cos(sqrt(2)sqrt(x)))/(sqrt(2)\sqrt{x)}
What is the first derivative of sin(sqrt(2x)) ?
The first derivative of sin(sqrt(2x)) is (cos(sqrt(2)sqrt(x)))/(sqrt(2)\sqrt{x)}