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

The derivative of ln((x^2)/(2x^2+3x+2)) is (3x+4)/(x(2x^2+3x+2))

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

The first derivative of ln((x^2)/(2x^2+3x+2)) is (3x+4)/(x(2x^2+3x+2))

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derivative of

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

\frac{3 x + 4}{x ( 2 x ^{2} + 3 x + 2 )}

Solution steps

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

Apply the chain rule:

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

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

\frac{d}{d x} (\frac{x ^{2}}{2 x ^{2} + 3 x + 2}) = \frac{3 x ^{2} + 4 x}{( 2 x ^{2} + 3 x + 2 ) ^{2}}

= \frac{1}{\frac{x ^{2}}{2 x ^{2} + 3 x + 2}} \cdot \frac{3 x ^{2} + 4 x}{( 2 x ^{2} + 3 x + 2 ) ^{2}}

Simplify

\frac{1}{\frac{x ^{2}}{2 x ^{2} + 3 x + 2}} \cdot \frac{3 x ^{2} + 4 x}{( 2 x ^{2} + 3 x + 2 ) ^{2}} : \frac{3 x + 4}{x ( 2 x ^{2} + 3 x + 2 )}

= \frac{3 x + 4}{x ( 2 x ^{2} + 3 x + 2 )}

\int x - 25 - x^{2} d x

\frac{\partial}{\partial x} (2 x^{4} + 3 y^{3} + 2 x y)

\int \frac{4 x ^{2} + 2 x - 1}{x ^{3} + x ^{2}} d x

\frac{d}{d x} (a - x)

\int 2 sin^{6} (x) cos (x) d x

What is the derivative of ln((x^2)/(2x^2+3x+2)) ?
The derivative of ln((x^2)/(2x^2+3x+2)) is (3x+4)/(x(2x^2+3x+2))
What is the first derivative of ln((x^2)/(2x^2+3x+2)) ?
The first derivative of ln((x^2)/(2x^2+3x+2)) is (3x+4)/(x(2x^2+3x+2))