What is the d/(dz)(sqrt(z+1)-1) ?

The d/(dz)(sqrt(z+1)-1) is 1/(2sqrt(z+1))

What is the first d/(dz)(sqrt(z+1)-1) ?

The first d/(dz)(sqrt(z+1)-1) is 1/(2sqrt(z+1))

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

\frac{1}{2 z + 1}

Solution steps

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

Apply the Sum/Difference Rule:

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

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

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

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

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

Simplify

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

What is the d/(dz)(sqrt(z+1)-1) ?
The d/(dz)(sqrt(z+1)-1) is 1/(2sqrt(z+1))
What is the first d/(dz)(sqrt(z+1)-1) ?
The first d/(dz)(sqrt(z+1)-1) is 1/(2sqrt(z+1))