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

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

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

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

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

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

Solution steps

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

Apply the chain rule:

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

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

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

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

Simplify

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

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

\int 1 - 2 cos (x) d x

\frac{13 e ^{6 x}}{x + 5}

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

\int \frac{5}{x + 4} d x

x \to 1 lim (\frac{3}{2} \cdot x - 1)

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