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

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

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

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

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Popular >

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

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

Solution steps

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

Apply the chain rule:

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

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

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

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

Simplify

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

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

\frac{\partial}{\partial x} (750 + 6 x - 7 y)

x^{2} - 3 x + 3, y = x

\int \frac{( ln ( x ) ) ^{44}}{x} d x

\int_{1}^{4} (x - 1) - (x^{2} - 4 x + 3) d x

\int cos (2 t) d t

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