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)}

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\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}}}

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

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

\int \frac{1}{( x + 4 )} d x

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

sin (\frac{2 t}{3})

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)}