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Popular >

derivative of xsin(x/2)

Solution

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

Solution

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

Solution steps

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

Apply the Product Rule:

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

f = x, g = sin (\frac{x}{2})

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

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

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

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

Simplify

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

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

Graph

Popular Examples

sum from n=0 to infinity of n*sin(1/n)

n = 0 \sum \infty n \cdot sin (\frac{1}{n})

(\partial)/(\partial x)(sec^2(xy))

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

sum from n=1 to infinity of 3/(pi^n)

n = 1 \sum \infty \frac{3}{π ^{n}}

derivative of x^{1/3}-x^{-2/3}derivative of

x^{\frac{1}{3}} - x^{- \frac{2}{3}}

limit as x approaches+0 of 2x^2cos(5/x)

x \to + 0 lim (2 x^{2} cos (\frac{5}{x}))

Frequently Asked Questions (FAQ)

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