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Popular >

derivative of sqrt(x)*sin(x)

Solution

\frac{d}{d x} (x \cdot 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

integral of 8x^3+1/(2x^2)

\int 8 x^{3} + \frac{1}{2 x ^{2}} d x

integral of e^{-cos(x)}sin^3(x)

\int e^{- c o s (x)} sin^{3} (x) d x

limit as x approaches 0 of cot(x)

x \to 0 lim (cot (x))

\frac{d}{d y} (2 y - 1)

y^{''}-2y^'+1y=0,y(0)=-1,y^'(0)=2

y^{^{''}} - 2 y^{^{'}} + 1 y = 0, y (0) = - 1, y^{^{'}} (0) = 2

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)