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

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

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

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

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derivative of

y = 2 x + 1

\frac{1}{2 x + 1}

Solution steps

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

Apply the chain rule:

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

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

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

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

Simplify

\frac{1}{2 2 x + 1} \cdot 2 : \frac{1}{2 x + 1}

= \frac{1}{2 x + 1}

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