What is (\partial)/(\partial x)((x^2)/(x+1)) ?

The answer to (\partial)/(\partial x)((x^2)/(x+1)) is (x^2+2x)/((x+1)^2)

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(\partial)/(\partial x)((x^2)/(x+1))

\frac{\partial}{\partial x} (\frac{x ^{2}}{x + 1})

\frac{x ^{2} + 2 x}{( x + 1 ) ^{2}}

Solution steps

\frac{\partial}{\partial x} (\frac{x ^{2}}{x + 1})

Apply the Quotient Rule:

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

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

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

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

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

Simplify

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

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

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

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

x^{2} + 3 x - 1

y^{^{''}} - 2 y^{^{'}} + y = 12 t e^{t} + 2 e^{t} + t - 4

\frac{d}{d x} (8 x - 2 x^{2})

What is (\partial)/(\partial x)((x^2)/(x+1)) ?
The answer to (\partial)/(\partial x)((x^2)/(x+1)) is (x^2+2x)/((x+1)^2)