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

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

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

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

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

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

Solution steps

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

Apply the Sum/Difference Rule:

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

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

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

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

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

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