What is the derivative of (4x+x^2-2)/((2+x)^2) ?

The derivative of (4x+x^2-2)/((2+x)^2) is (12)/((2+x)^3)

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

The first derivative of (4x+x^2-2)/((2+x)^2) is (12)/((2+x)^3)

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derivative of

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

\frac{12}{( 2 + x ) ^{3}}

Solution steps

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

Apply the Quotient Rule:

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

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

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

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

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

Simplify

\frac{( 2 x + 4 ) ( 2 + x ) ^{2} - 2 ( 2 + x ) ( 4 x + x ^{2} - 2 )}{( ( 2 + x ) ^{2} ) ^{2}} : \frac{12}{( 2 + x ) ^{3}}

= \frac{12}{( 2 + x ) ^{3}}

\frac{d}{d x} (\frac{3 x ^{2} - 5}{2 x ^{2} + 1})

x \to - 8 + lim (\frac{( x + 7 )}{x + 8})

\frac{d}{d x} (e^{- a ∣ x ∣})

\int \frac{2 x}{( x ^{2} + 1 ) ^{90}} d x

f (8) = 2 (x - 5)

What is the derivative of (4x+x^2-2)/((2+x)^2) ?
The derivative of (4x+x^2-2)/((2+x)^2) is (12)/((2+x)^3)
What is the first derivative of (4x+x^2-2)/((2+x)^2) ?
The first derivative of (4x+x^2-2)/((2+x)^2) is (12)/((2+x)^3)