What is the derivative of x^{-1/2}*cos(x) ?

The derivative of x^{-1/2}*cos(x) is -(cos(x))/(2x^{3/2)}-(sin(x))/(x^{1/2)}

What is the first derivative of x^{-1/2}*cos(x) ?

The first derivative of x^{-1/2}*cos(x) is -(cos(x))/(2x^{3/2)}-(sin(x))/(x^{1/2)}

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

\frac{d}{d x} (x^{- \frac{1}{2}} \cdot cos (x))

- \frac{cos ( x )}{2 x ^{\frac{3}{2}}} - \frac{sin ( x )}{x ^{\frac{1}{2}}}

Solution steps

\frac{d}{d x} (x^{- \frac{1}{2}} cos (x))

Apply the Product Rule:

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

f = x^{- \frac{1}{2}}, g = cos (x)

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

\frac{d}{d x} (x^{- \frac{1}{2}}) = - \frac{1}{2 x ^{\frac{3}{2}}}

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

= (- \frac{1}{2 x ^{\frac{3}{2}}}) cos (x) + (- sin (x)) x^{- \frac{1}{2}}

Simplify

(- \frac{1}{2 x ^{\frac{3}{2}}}) cos (x) + (- sin (x)) x^{- \frac{1}{2}} : - \frac{cos ( x )}{2 x ^{\frac{3}{2}}} - \frac{sin ( x )}{x ^{\frac{1}{2}}}

= - \frac{cos ( x )}{2 x ^{\frac{3}{2}}} - \frac{sin ( x )}{x ^{\frac{1}{2}}}

What is the derivative of x^{-1/2}*cos(x) ?
The derivative of x^{-1/2}*cos(x) is -(cos(x))/(2x^{3/2)}-(sin(x))/(x^{1/2)}
What is the first derivative of x^{-1/2}*cos(x) ?
The first derivative of x^{-1/2}*cos(x) is -(cos(x))/(2x^{3/2)}-(sin(x))/(x^{1/2)}