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

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

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

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

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derivative of

f (x) = 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 )}

f (x) = 3 x - 6 x

\int_{1}^{x} \frac{1}{x} d x

\int 4 sin^{2} (π x) cos^{5} (π x) d x

\int_{0}^{1} x \cdot e^{x^{2}} d x

\int_{0}^{1} (2 x^{2} - 1) d x

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