What is the derivative of 6x^{-1/2} ?

The derivative of 6x^{-1/2} is -3/(x^{3/2)}

What is the first derivative of 6x^{-1/2} ?

The first derivative of 6x^{-1/2} is -3/(x^{3/2)}

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\frac{d}{d x} (6 x^{- \frac{1}{2}})

- \frac{3}{x ^{\frac{3}{2}}}

Solution steps

\frac{d}{d x} (6 x^{- \frac{1}{2}})

Take the constant out:

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

= 6 \frac{d}{d x} (x^{- \frac{1}{2}})

Apply the Power Rule:

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

= 6 (- \frac{1}{2} x^{- \frac{1}{2} - 1})

Simplify

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

= - \frac{3}{x ^{\frac{3}{2}}}

What is the derivative of 6x^{-1/2} ?
The derivative of 6x^{-1/2} is -3/(x^{3/2)}
What is the first derivative of 6x^{-1/2} ?
The first derivative of 6x^{-1/2} is -3/(x^{3/2)}