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Popular >

derivative of f(x)=sqrt(x)sin(x)

Solution

derivative of

f (x) = 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

y^{''}+1/4 y^'+2y=2cos(4123t)

y^{^{''}} + \frac{1}{4} y^{^{'}} + 2 y = 2 cos (4123 t)

integral of (sqrt(1-4x^2))/x

\int \frac{1 - 4 x ^{2}}{x} d x

derivative of (2x^2+2x+6/(sqrt(x)))

\frac{d}{d x} (\frac{2 x ^{2} + 2 x + 6}{x})

derivative of 2/(3t^2)derivative of

\frac{2}{3 t ^{2}}

integral of 1/2 x^4

\int \frac{1}{2} x^{4} d x

Frequently Asked Questions (FAQ)

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