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

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

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

The first derivative of 1+sqrt(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) + \frac{d}{d x} (x - 1)

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

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

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

Simplify

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

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