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

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

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

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

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derivative

\frac{1}{2 x + 1}

Solution steps

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

Apply the chain rule:

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

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

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

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

Simplify

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

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