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Popular >

derivative of ln((4x/(x+9)))

Solution

\frac{d}{d x} (ln (\frac{4 x}{x + 9}))

Solution

\frac{9}{x ( x + 9 )}

Solution steps

\frac{d}{d x} (ln (\frac{4 x}{x + 9}))

Apply the chain rule:

\frac{1}{\frac{4 x}{x + 9}} \frac{d}{d x} (\frac{4 x}{x + 9})

= \frac{1}{\frac{4 x}{x + 9}} \frac{d}{d x} (\frac{4 x}{x + 9})

\frac{d}{d x} (\frac{4 x}{x + 9}) = \frac{36}{( x + 9 ) ^{2}}

= \frac{1}{\frac{4 x}{x + 9}} \cdot \frac{36}{( x + 9 ) ^{2}}

Simplify

\frac{1}{\frac{4 x}{x + 9}} \cdot \frac{36}{( x + 9 ) ^{2}} : \frac{9}{x ( x + 9 )}

= \frac{9}{x ( x + 9 )}

Popular Examples

integral from 0 to 2 of sqrt(1+9x)

\int_{0}^{2} 1 + 9 x d x

integral from 6 to 9 of 1/(9+(x-6)^2)

\int_{6}^{9} \frac{1}{9 + ( x - 6 ) ^{2}} d x

derivative of x+c

\frac{d}{d x} (x + c)

derivative of x^4sin(xcos(x))

\frac{d}{d x} (x^{4} sin (x) cos (x))

integral from 0 to 1 of 6^x

\int_{0}^{1} 6^{x} d x

Frequently Asked Questions (FAQ)

What is the derivative of ln((4x/(x+9))) ?
The derivative of ln((4x/(x+9))) is 9/(x(x+9))
What is the first derivative of ln((4x/(x+9))) ?
The first derivative of ln((4x/(x+9))) is 9/(x(x+9))