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

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

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

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

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

Solution steps

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

Apply the chain rule:

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

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

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

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

Simplify

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

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

x \to 1 + lim (arctan (ln (x)))

\frac{9 x}{3 x + 7}

\int sin^{2} (2 x) sin (x) d x

sin (tan (9 x))

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