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

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

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

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

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derivative of

ln (x x^{2} + 1)

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

Solution steps

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

Apply the chain rule:

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

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

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

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

Simplify

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

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

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\int_{1}^{2} x e^{x^{2}} d x

\frac{d y}{d x} = (4 y)

\frac{d}{d x} ((3 x^{2} + 4) (2 x - 3))

\int \frac{5}{x} + e^{x} d x

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