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

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

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

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

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

\frac{1}{2 x + 1}

Solution steps

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

Apply the Sum/Difference Rule:

(f \pm g)^{'} = f^{'} \pm g^{'}

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

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

\frac{d}{d x} (1) = 0

= \frac{1}{2 1 + x} - 0

Simplify

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

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