What is the derivative of y=sqrt(2x-1/2) ?

The derivative of y=sqrt(2x-1/2) is sqrt(2/(4x-1))

What is the first derivative of y=sqrt(2x-1/2) ?

The first derivative of y=sqrt(2x-1/2) is sqrt(2/(4x-1))

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derivative of

y = 2 x - \frac{1}{2}

\frac{2}{4 x - 1}

Solution steps

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

Apply the chain rule:

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

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

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

= \frac{1}{2 2 x - \frac{1}{2}} \cdot 2

Simplify

\frac{1}{2 2 x - \frac{1}{2}} \cdot 2 : \frac{2}{4 x - 1}

= \frac{2}{4 x - 1}

What is the derivative of y=sqrt(2x-1/2) ?
The derivative of y=sqrt(2x-1/2) is sqrt(2/(4x-1))
What is the first derivative of y=sqrt(2x-1/2) ?
The first derivative of y=sqrt(2x-1/2) is sqrt(2/(4x-1))