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

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

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

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

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derivative of

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

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

Solution steps

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

Apply the chain rule:

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

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

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

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

Simplify

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

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

\frac{\partial}{\partial y} (2 (x + y))

\frac{\partial}{\partial x} (\frac{2 x - y}{x + 3 y})

x \to 2 - lim (x + c)

\int x - \frac{2}{x} d x

\int sec^{2} (θ) tan (θ) d θ

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