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

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

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

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

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

2 x

Solution steps

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

Apply the chain rule:

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

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

\frac{d}{d x} ((x^{2} + 1)^{2}) = 4 x (x^{2} + 1)

= \frac{1}{2 ( x ^{2} + 1 ) ^{2}} \cdot 4 x (x^{2} + 1)

Simplify

\frac{1}{2 ( x ^{2} + 1 ) ^{2}} \cdot 4 x (x^{2} + 1) : 2 x

= 2 x

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