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Popular >

derivative of 1/2 xsin(x)

Solution

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

Solution

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

Solution steps

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

Take the constant out:

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

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

Apply the Product Rule:

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

f = x, g = sin (x)

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

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

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

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

Simplify

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

Popular Examples

integral of 9tsec^2(2t)

\int 9 t sec^{2} (2 t) d t

integral of 7sin^2(x)cos^3(x)

\int 7 sin^{2} (x) cos^{3} (x) d x

sum from n=0 to infinity of (8^n)/(n!)

n = 0 \sum \infty \frac{8 ^{n}}{n !}

laplacetransform e^{2t}sin(t)laplace transform

e^{2 t} sin (t)

implicit (dy)/(dx),y= 3/x implicit derivative

\frac{d y}{d x}, y = \frac{3}{x}

Frequently Asked Questions (FAQ)

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