What is (\partial)/(\partial x)(sqrt(1+x^2)) ?

The answer to (\partial)/(\partial x)(sqrt(1+x^2)) is x/(sqrt(1+x^2))

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(\partial)/(\partial x)(sqrt(1+x^2))

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

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

Solution steps

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

Apply the chain rule:

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

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

\frac{\partial}{\partial 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}}

x \to 2 π lim (ln (cos (x)))

4 x sin (x)

\int \frac{1}{sec ( 2 x )} d x

x \to 11 + lim (x - 11)

\frac{d y}{d x} = sin (2 x) - \frac{1}{2} sin (4 x)

What is (\partial)/(\partial x)(sqrt(1+x^2)) ?
The answer to (\partial)/(\partial x)(sqrt(1+x^2)) is x/(sqrt(1+x^2))