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

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

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

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

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derivative of

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

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

Solution steps

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

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

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

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

Simplify

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

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

\frac{\partial}{\partial x} (x y + \frac{1}{x} + \frac{1}{y})

f (x) = 9 - 6 x, at x = - 1

- \frac{3}{s + 3} + \frac{4}{s - 4}

\int \frac{8}{x ^{- 1} + 2} d x

y = 4 x^{2} - x

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