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

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

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

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

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derivative of

1 + x^{2}

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

Solution steps

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

Apply the chain rule:

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

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

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

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

Simplify

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

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

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

y = 3 x^{2} + 5

\int \frac{2}{5 cos ^{2} ( x )} d x

\int sec (2 x) tan^{3} (2 x) d x

e^{\frac{x ^{2}}{2}}

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