What is the derivative of (20x/(x^2+2)) ?

The derivative of (20x/(x^2+2)) is (20(-x^2+2))/((x^2+2)^2)

What is the first derivative of (20x/(x^2+2)) ?

The first derivative of (20x/(x^2+2)) is (20(-x^2+2))/((x^2+2)^2)

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\frac{d}{d x} (\frac{20 x}{x ^{2} + 2})

\frac{20 ( - x ^{2} + 2 )}{( x ^{2} + 2 ) ^{2}}

Solution steps

\frac{d}{d x} (\frac{20 x}{x ^{2} + 2})

Take the constant out:

(a \cdot f)^{'} = a \cdot f^{'}

= 20 \frac{d}{d x} (\frac{x}{x ^{2} + 2})

Apply the Quotient Rule:

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

= 20 \cdot \frac{\frac{d x}{d x} ( x ^{2} + 2 ) - \frac{d}{d x} ( x ^{2} + 2 ) x}{( x ^{2} + 2 ) ^{2}}

\frac{d x}{d x} = 1

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

= 20 \cdot \frac{1 \cdot ( x ^{2} + 2 ) - 2 xx}{( x ^{2} + 2 ) ^{2}}

Simplify

20 \cdot \frac{1 \cdot ( x ^{2} + 2 ) - 2 xx}{( x ^{2} + 2 ) ^{2}} : \frac{20 ( - x ^{2} + 2 )}{( x ^{2} + 2 ) ^{2}}

= \frac{20 ( - x ^{2} + 2 )}{( x ^{2} + 2 ) ^{2}}

x \to 3 lim (\frac{2}{x - 2})

\frac{( e ^{- 2 s} - 2 )}{s}

\int x o t x^{2} d x

\frac{\partial}{\partial x} (1 + e^{x})

\frac{d}{d x} (\frac{1}{x \cdot ln ( x ^{9} )})

What is the derivative of (20x/(x^2+2)) ?
The derivative of (20x/(x^2+2)) is (20(-x^2+2))/((x^2+2)^2)
What is the first derivative of (20x/(x^2+2)) ?
The first derivative of (20x/(x^2+2)) is (20(-x^2+2))/((x^2+2)^2)