What is the derivative of ln((x^3+4/(2x))) ?

The derivative of ln((x^3+4/(2x))) is (2(x^3-2))/(x(x^3+4))

What is the first derivative of ln((x^3+4/(2x))) ?

The first derivative of ln((x^3+4/(2x))) is (2(x^3-2))/(x(x^3+4))

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

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

Solution steps

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

Apply the chain rule:

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

= \frac{1}{\frac{x ^{3} + 4}{2 x}} \frac{d}{d x} (\frac{x ^{3} + 4}{2 x})

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

= \frac{1}{\frac{x ^{3} + 4}{2 x}} \cdot \frac{x ^{3} - 2}{x ^{2}}

Simplify

\frac{1}{\frac{x ^{3} + 4}{2 x}} \cdot \frac{x ^{3} - 2}{x ^{2}} : \frac{2 ( x ^{3} - 2 )}{x ( x ^{3} + 4 )}

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

What is the derivative of ln((x^3+4/(2x))) ?
The derivative of ln((x^3+4/(2x))) is (2(x^3-2))/(x(x^3+4))
What is the first derivative of ln((x^3+4/(2x))) ?
The first derivative of ln((x^3+4/(2x))) is (2(x^3-2))/(x(x^3+4))