What is the derivative of ln((9x/(x^2+15))) ?

The derivative of ln((9x/(x^2+15))) is (-x^2+15)/(x(x^2+15))

What is the first derivative of ln((9x/(x^2+15))) ?

The first derivative of ln((9x/(x^2+15))) is (-x^2+15)/(x(x^2+15))

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\frac{d}{d x} (ln (\frac{9 x}{x ^{2} + 15}))

\frac{- x ^{2} + 15}{x ( x ^{2} + 15 )}

Solution steps

\frac{d}{d x} (ln (\frac{9 x}{x ^{2} + 15}))

Apply the chain rule:

\frac{1}{\frac{9 x}{x ^{2} + 15}} \frac{d}{d x} (\frac{9 x}{x ^{2} + 15})

= \frac{1}{\frac{9 x}{x ^{2} + 15}} \frac{d}{d x} (\frac{9 x}{x ^{2} + 15})

\frac{d}{d x} (\frac{9 x}{x ^{2} + 15}) = \frac{9 ( - x ^{2} + 15 )}{( x ^{2} + 15 ) ^{2}}

= \frac{1}{\frac{9 x}{x ^{2} + 15}} \cdot \frac{9 ( - x ^{2} + 15 )}{( x ^{2} + 15 ) ^{2}}

Simplify

\frac{1}{\frac{9 x}{x ^{2} + 15}} \cdot \frac{9 ( - x ^{2} + 15 )}{( x ^{2} + 15 ) ^{2}} : \frac{- x ^{2} + 15}{x ( x ^{2} + 15 )}

= \frac{- x ^{2} + 15}{x ( x ^{2} + 15 )}

\frac{d}{d x} (\frac{cos ( x )}{x ^{7}})

\frac{d}{d x} ((5 x - 4)^{3})

\int x - 4 d x

\int e^{- x} \cdot x^{- 1} d x

\frac{d}{d x} (\frac{1}{9 + x ^{2}})

What is the derivative of ln((9x/(x^2+15))) ?
The derivative of ln((9x/(x^2+15))) is (-x^2+15)/(x(x^2+15))
What is the first derivative of ln((9x/(x^2+15))) ?
The first derivative of ln((9x/(x^2+15))) is (-x^2+15)/(x(x^2+15))