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

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

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

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

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

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

Solution steps

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

Take the constant out:

(a \cdot f)^{'} = a \cdot f^{'}

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

Apply the Product Rule:

(f \cdot g)^{'} = f^{'} \cdot g + f \cdot g^{'}

f = sin (x), g = cos (x)

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

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

\frac{d}{d x} (cos (x)) = - sin (x)

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

Simplify

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

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

(\frac{1}{y ^{2}} - \frac{7}{y ^{4}}) (y + 5 y^{3})

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

f (x) = - 1

\frac{d}{d z} (\frac{x}{y} - y z)

x \to 2 - lim (cos (\frac{1}{x - 2}))

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