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

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

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

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

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

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

Solution steps

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

Apply the Quotient Rule:

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

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

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

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

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

Simplify

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

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

x (\frac{d y}{d x}) + y = 4 x + 1

x - 4

y = sin (x), y = 3 x, x = \frac{π}{2}, x = π

f (x) = \frac{- 4}{x ^{3}}

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