What is the derivative of (6x+2x^2)/((3+2x)^2) ?

The derivative of (6x+2x^2)/((3+2x)^2) is (18)/((3+2x)^3)

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

The first derivative of (6x+2x^2)/((3+2x)^2) is (18)/((3+2x)^3)

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derivative of

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

\frac{18}{( 3 + 2 x ) ^{3}}

Solution steps

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

Apply the Quotient Rule:

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

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

\frac{d}{d x} (6 x + 2 x^{2}) = 6 + 4 x

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

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

Simplify

\frac{( 6 + 4 x ) ( 3 + 2 x ) ^{2} - 4 ( 3 + 2 x ) ( 6 x + 2 x ^{2} )}{( ( 3 + 2 x ) ^{2} ) ^{2}} : \frac{18}{( 3 + 2 x ) ^{3}}

= \frac{18}{( 3 + 2 x ) ^{3}}

\int \frac{x + 1}{x ^{2} - 9} d x

\frac{\partial}{\partial x} (- 3 x^{2} y^{3} sin (x^{3} y^{3}))

f (0) = \frac{x}{x ^{2} + 1}

\int e^{- 0.01 t} d t

\frac{d}{d x} (\frac{1}{1 + ∣ x ∣} + \frac{1}{1 + ∣ x - 3 ∣})

What is the derivative of (6x+2x^2)/((3+2x)^2) ?
The derivative of (6x+2x^2)/((3+2x)^2) is (18)/((3+2x)^3)
What is the first derivative of (6x+2x^2)/((3+2x)^2) ?
The first derivative of (6x+2x^2)/((3+2x)^2) is (18)/((3+2x)^3)