What is the derivative of (x^2+1)^{1/2}-1 ?

The derivative of (x^2+1)^{1/2}-1 is x/((x^2+1)^{1/2)}

What is the first derivative of (x^2+1)^{1/2}-1 ?

The first derivative of (x^2+1)^{1/2}-1 is x/((x^2+1)^{1/2)}

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derivative of

(x^{2} + 1)^{\frac{1}{2}} - 1

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

Solution steps

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

Apply the Sum/Difference Rule:

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

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

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

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

= \frac{x}{( x ^{2} + 1 ) ^{\frac{1}{2}}} - 0

Simplify

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

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