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

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

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

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

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

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

Solution steps

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

Apply the Sum/Difference Rule:

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

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

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

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

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

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