What is the derivative of sqrt(x)cos(sqrt(x)) ?

The derivative of sqrt(x)cos(sqrt(x)) is (cos(sqrt(x))}{2sqrt(x)}-\frac{sin(sqrt(x)))/2

What is the first derivative of sqrt(x)cos(sqrt(x)) ?

The first derivative of sqrt(x)cos(sqrt(x)) is (cos(sqrt(x))}{2sqrt(x)}-\frac{sin(sqrt(x)))/2

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

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

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

Solution steps

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

Apply the Product Rule:

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

f = x, g = cos (x)

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

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

\frac{d}{d x} (cos (x)) = - \frac{sin ( x )}{2 x}

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

Simplify

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

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

\int \frac{y - 1}{y + 4} d y

x \to 3 lim (6 x^{2})

\int 8 sec^{3} (6 x) d x

\frac{\partial}{\partial x} (3 e^{2 x} - 5 ln (y) + 7)

\int_{2}^{7} x d x

What is the derivative of sqrt(x)cos(sqrt(x)) ?
The derivative of sqrt(x)cos(sqrt(x)) is (cos(sqrt(x))}{2sqrt(x)}-\frac{sin(sqrt(x)))/2
What is the first derivative of sqrt(x)cos(sqrt(x)) ?
The first derivative of sqrt(x)cos(sqrt(x)) is (cos(sqrt(x))}{2sqrt(x)}-\frac{sin(sqrt(x)))/2