What is the derivative of 8/(((x-2)^{1/2))} ?

The derivative of 8/(((x-2)^{1/2))} is -4/((x-2)^{3/2)}

What is the first derivative of 8/(((x-2)^{1/2))} ?

The first derivative of 8/(((x-2)^{1/2))} is -4/((x-2)^{3/2)}

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derivative

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

Solution steps

\frac{d}{d x} (\frac{8}{( x - 2 ) ^{\frac{1}{2}}})

Take the constant out:

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

= 8 \frac{d}{d x} (\frac{1}{( x - 2 ) ^{\frac{1}{2}}})

Apply exponent rule:

\frac{1}{a} = a^{- 1}

= 8 \frac{d}{d x} ((x - 2)^{- \frac{1}{2}})

Apply the chain rule:

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

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

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

= 8 (- \frac{1}{2 ( x - 2 ) ^{\frac{3}{2}}} \cdot 1)

Simplify

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

= - \frac{4}{( x - 2 ) ^{\frac{3}{2}}}

What is the derivative of 8/(((x-2)^{1/2))} ?
The derivative of 8/(((x-2)^{1/2))} is -4/((x-2)^{3/2)}
What is the first derivative of 8/(((x-2)^{1/2))} ?
The first derivative of 8/(((x-2)^{1/2))} is -4/((x-2)^{3/2)}