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

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

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

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

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derivative of

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

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

Solution steps

\frac{d}{d x} ((2 x - 4)^{\frac{1}{2}})

Apply the chain rule:

\frac{1}{2 ( 2 x - 4 ) ^{\frac{1}{2}}} \frac{d}{d x} (2 x - 4)

= \frac{1}{2 ( 2 x - 4 ) ^{\frac{1}{2}}} \frac{d}{d x} (2 x - 4)

\frac{d}{d x} (2 x - 4) = 2

= \frac{1}{2 ( 2 x - 4 ) ^{\frac{1}{2}}} \cdot 2

Simplify

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

= \frac{1}{( 2 x - 4 ) ^{\frac{1}{2}}}

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