What is the derivative of-1/2 x^{-3/2} ?

The derivative of-1/2 x^{-3/2} is 3/(4x^{5/2)}

What is the first derivative of-1/2 x^{-3/2} ?

The first derivative of-1/2 x^{-3/2} is 3/(4x^{5/2)}

Popular >

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

\frac{3}{4 x ^{\frac{5}{2}}}

Solution steps

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

Take the constant out:

(a \cdot f)^{'} = a \cdot f^{'}

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

Apply the Power Rule:

\frac{d}{d x} (x^{a}) = a \cdot x^{a - 1}

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

Simplify

- \frac{1}{2} (- \frac{3}{2} x^{- \frac{3}{2} - 1}) : \frac{3}{4 x ^{\frac{5}{2}}}

= \frac{3}{4 x ^{\frac{5}{2}}}

y^{^{''}} - 2 y^{^{'}} + 5 y = e^{x} sin (2 x)

y^{^{'}} + y (\frac{3}{x} + \frac{x}{2}) = 0

f (x) = \frac{1}{7 x - 4}

x^{3} + x + 12 x^{\frac{1}{2}}

\frac{d}{d x} ((5 x + 1)^{3} (6 x^{2} + 3 x + 2)^{5})

What is the derivative of-1/2 x^{-3/2} ?
The derivative of-1/2 x^{-3/2} is 3/(4x^{5/2)}
What is the first derivative of-1/2 x^{-3/2} ?
The first derivative of-1/2 x^{-3/2} is 3/(4x^{5/2)}