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

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

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

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

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

Solution steps

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

Apply the Quotient Rule:

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

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

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

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

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

1 \cdot (x + 1) - 1 \cdot x = 1

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

x \to \infty lim (x (1)^{x})

\int e^{8 θ} sin (9 θ) d θ

12 e^{x}

\frac{x ^{2} + x - 2}{x ^{3} + 6}

y = \frac{x ^{2} - 4}{x - 3}

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