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

The derivative of ((x^2+3x))/((2x+3)^3) is (-2x^2-6x+9)/((2x+3)^4)

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

The first derivative of ((x^2+3x))/((2x+3)^3) is (-2x^2-6x+9)/((2x+3)^4)

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derivative of

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

\frac{- 2 x ^{2} - 6 x + 9}{( 2 x + 3 ) ^{4}}

Solution steps

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

Apply the Quotient Rule:

(\frac{f}{g})^{'} = \frac{f ^{'} \cdot g - g ^{'} \cdot f}{g ^{2}}

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

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

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

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

Simplify

\frac{( 2 x + 3 ) ( 2 x + 3 ) ^{3} - 6 ( 2 x + 3 ) ^{2} ( x ^{2} + 3 x )}{( ( 2 x + 3 ) ^{3} ) ^{2}} : \frac{- 2 x ^{2} - 6 x + 9}{( 2 x + 3 ) ^{4}}

= \frac{- 2 x ^{2} - 6 x + 9}{( 2 x + 3 ) ^{4}}

\int ln (x + x^{2}) d x

\int x^{2} (7 - x^{3})^{\frac{2}{3}} d x

\frac{d}{d x} (tan (x^{2} - 4 x))

x \to - \infty lim (x^{3} - 5 x^{2})

\int x^{2} \cdot x - 5 d x

What is the derivative of ((x^2+3x))/((2x+3)^3) ?
The derivative of ((x^2+3x))/((2x+3)^3) is (-2x^2-6x+9)/((2x+3)^4)
What is the first derivative of ((x^2+3x))/((2x+3)^3) ?
The first derivative of ((x^2+3x))/((2x+3)^3) is (-2x^2-6x+9)/((2x+3)^4)