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

The derivative of (2x^2+4x/(2+x^2)) is (-4x^2+8x+8)/((2+x^2)^2)

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

The first derivative of (2x^2+4x/(2+x^2)) is (-4x^2+8x+8)/((2+x^2)^2)

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

\frac{- 4 x ^{2} + 8 x + 8}{( 2 + x ^{2} ) ^{2}}

Solution steps

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

Apply the Quotient Rule:

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

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

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

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

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

Expand

(4 x + 4) (2 + x^{2}) - 2 x (2 x^{2} + 4 x) : - 4 x^{2} + 8 x + 8

= \frac{- 4 x ^{2} + 8 x + 8}{( 2 + x ^{2} ) ^{2}}

\int cos (t) sin (t) d t

\frac{2 x ^{2} - 5 x + 5}{x - 2}

\frac{d}{d x} (f (x) sin (x))

x \to 0 lim (\frac{x}{8 x ^{2} - x})

\frac{d}{d x} (\frac{x - a}{1 + x})

What is the derivative of (2x^2+4x/(2+x^2)) ?
The derivative of (2x^2+4x/(2+x^2)) is (-4x^2+8x+8)/((2+x^2)^2)
What is the first derivative of (2x^2+4x/(2+x^2)) ?
The first derivative of (2x^2+4x/(2+x^2)) is (-4x^2+8x+8)/((2+x^2)^2)