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Popular >

derivative of ln((3x/(2x+1)))

Solution

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

Solution

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

Solution steps

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

Apply the chain rule:

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

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

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

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

Simplify

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

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

Popular Examples

integral of 1/((x+2)(x+7)(2x-5)(x+1)^2)

\int \frac{1}{( x + 2 ) ( x + 7 ) ( 2 x - 5 ) ( x + 1 ) ^{2}} d x

area y=xe^{-0.4x},x=5,y=0 area

y = x e^{- 0.4 x}, x = 5, y = 0

derivative of 2+sin(x)

\frac{d}{d x} (2 + sin (x))

limit as x approaches 5+of (x-5)/(x-5)

x \to 5 + lim (\frac{x - 5}{x - 5})

limit as x approaches 0 of sqrt(x)ln(x)

x \to 0 lim (x ln (x))

Frequently Asked Questions (FAQ)

What is the derivative of ln((3x/(2x+1))) ?
The derivative of ln((3x/(2x+1))) is 1/(x(2x+1))
What is the first derivative of ln((3x/(2x+1))) ?
The first derivative of ln((3x/(2x+1))) is 1/(x(2x+1))