What is the derivative of sqrt(x^2+1)-x ?

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

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

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

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

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

Solution steps

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

Apply the Sum/Difference Rule:

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

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

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

\frac{d x}{d x} = 1

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

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