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Popular >

derivative of log_{e}(x^2+1)

Solution

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

Solution

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

Solution steps

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

Simplify

lo g_{e} (x^{2} + 1) : ln (x^{2} + 1)

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

Apply the chain rule:

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

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

\frac{d}{d 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}

Popular Examples

integral of (e^{3x})/(sqrt(1-e^{6x))}

\int \frac{e ^{3 x}}{1 - e ^{6 x}} d x

limit as x approaches infinity of (5-2x^{3/2})/(3x-4)

x \to \infty lim (\frac{5 - 2 x ^{\frac{3}{2}}}{3 x - 4})

integral of (1-x)(2+x^2)

\int (1 - x) (2 + x^{2}) d x

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arctan (\frac{7}{x ^{2}})

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Frequently Asked Questions (FAQ)

What is the derivative of log_{e}(x^2+1) ?
The derivative of log_{e}(x^2+1) is (2x)/(x^2+1)
What is the first derivative of log_{e}(x^2+1) ?
The first derivative of log_{e}(x^2+1) is (2x)/(x^2+1)