en

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

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)

Graph

Popular Examples

integral of xe^{x^2}sin(x^2)

\int x e^{x^{2}} sin (x^{2}) d x

derivative of y=log_{3}(x^2+1)derivative of

y = lo g_{3} (x^{2} + 1)

(dy}{dx}=\frac{26)/x

\frac{d y}{d x} = \frac{26}{x}

derivative of f(x)=x^4+9x derivative of

f (x) = x^{4} + 9 x

integral of cos(x)sin(y)

\int cos (x) sin (y) 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)