What is the derivative of 1/2 x+1/4 sin(2x) ?

The derivative of 1/2 x+1/4 sin(2x) is 1/2+1/2 cos(2x)

What is the first derivative of 1/2 x+1/4 sin(2x) ?

The first derivative of 1/2 x+1/4 sin(2x) is 1/2+1/2 cos(2x)

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\frac{d}{d x} (\frac{1}{2} x + \frac{1}{4} sin (2 x))

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

Solution steps

\frac{d}{d x} (\frac{1}{2} x + \frac{1}{4} sin (2 x))

Simplify

\frac{1}{2} x + \frac{1}{4} sin (2 x) : \frac{x}{2} + \frac{1}{4} sin (2 x)

= \frac{d}{d x} (\frac{x}{2} + \frac{1}{4} sin (2 x))

Apply the Sum/Difference Rule:

(f \pm g)^{'} = f^{'} \pm g^{'}

= \frac{d}{d x} (\frac{x}{2}) + \frac{d}{d x} (\frac{1}{4} sin (2 x))

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

\frac{d}{d x} (\frac{1}{4} sin (2 x)) = \frac{1}{2} cos (2 x)

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

What is the derivative of 1/2 x+1/4 sin(2x) ?
The derivative of 1/2 x+1/4 sin(2x) is 1/2+1/2 cos(2x)
What is the first derivative of 1/2 x+1/4 sin(2x) ?
The first derivative of 1/2 x+1/4 sin(2x) is 1/2+1/2 cos(2x)