What is the derivative of y= 1/2 x+1/4 xsin(2x) ?

The derivative of y= 1/2 x+1/4 xsin(2x) is (1+xcos(2x))/2+1/4 sin(2x)

What is the first derivative of y= 1/2 x+1/4 xsin(2x) ?

The first derivative of y= 1/2 x+1/4 xsin(2x) is (1+xcos(2x))/2+1/4 sin(2x)

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derivative of

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

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

Solution steps

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

Simplify

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

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

Apply the Sum/Difference Rule:

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

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

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

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

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

Simplify

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

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

f (x) = x x, at x = 4

\int \frac{( e ^{x} )}{e ^{x} ( e ^{x} - 3 )} d x

\int \frac{( x ^{3} )}{x ^{2} + 81} d x

x^{2} sin (x)

\int \frac{arctan ( 3 x )}{1 + 9 x ^{2}} d x

What is the derivative of y= 1/2 x+1/4 xsin(2x) ?
The derivative of y= 1/2 x+1/4 xsin(2x) is (1+xcos(2x))/2+1/4 sin(2x)
What is the first derivative of y= 1/2 x+1/4 xsin(2x) ?
The first derivative of y= 1/2 x+1/4 xsin(2x) is (1+xcos(2x))/2+1/4 sin(2x)