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Popular >

derivative of sqrt(x)sin(x)

Solution

derivative of

x sin (x)

Solution

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

Solution steps

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

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

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

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

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

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

Popular Examples

derivative of f(x)=sqrt(1+8x)derivative of

f (x) = 1 + 8 x

derivative of (1+x^4)^{2/3}derivative of

(1 + x^{4})^{\frac{2}{3}}

derivative of ((5x-3)/((4x-3/x)))

\frac{d}{d x} (\frac{( 5 x - 3 )}{( 4 x - \frac{3}{x} )})

(\partial)/(\partial x)(y(-14x-4y+1))

\frac{\partial}{\partial x} (y (- 14 x - 4 y + 1))

integral of x(x^2+3)^2

\int x (x^{2} + 3)^{2} d x

Frequently Asked Questions (FAQ)

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