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

The derivative of ln((x^2)/(3-x)) is (6-x)/(x(-x+3))

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

The first derivative of ln((x^2)/(3-x)) is (6-x)/(x(-x+3))

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derivative of

ln (\frac{x ^{2}}{3 - x})

\frac{6 - x}{x ( - x + 3 )}

Solution steps

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

Apply the chain rule:

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

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

\frac{d}{d x} (\frac{x ^{2}}{3 - x}) = \frac{6 x - x ^{2}}{( 3 - x ) ^{2}}

= \frac{1}{\frac{x ^{2}}{3 - x}} \cdot \frac{6 x - x ^{2}}{( 3 - x ) ^{2}}

Simplify

\frac{1}{\frac{x ^{2}}{3 - x}} \cdot \frac{6 x - x ^{2}}{( 3 - x ) ^{2}} : \frac{6 - x}{x ( - x + 3 )}

= \frac{6 - x}{x ( - x + 3 )}

What is the derivative of ln((x^2)/(3-x)) ?
The derivative of ln((x^2)/(3-x)) is (6-x)/(x(-x+3))
What is the first derivative of ln((x^2)/(3-x)) ?
The first derivative of ln((x^2)/(3-x)) is (6-x)/(x(-x+3))