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

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

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

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

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

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

Solution steps

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

Simplify

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

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

Take the constant out:

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

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

Apply the Product Rule:

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

f = x, g = cos (x)

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

\frac{d x}{d x} = 1

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

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

Simplify

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

\int \frac{9}{x ^{- 1} + 3} d x

\frac{\partial}{\partial x} (y cos (x^{2} y))

(8 \frac{1}{7}, 9), (4, 3 \frac{1}{5})

y = ln (x^{2} - 5 x + 1), (5, 0)

\int_{0}^{\frac{π}{3}} x sin (6 x) d x

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