What is (\partial)/(\partial x)(x/(x+3)) ?

The answer to (\partial)/(\partial x)(x/(x+3)) is 3/((x+3)^2)

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(\partial)/(\partial x)(x/(x+3))

\frac{\partial}{\partial x} (\frac{x}{x + 3})

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

Solution steps

\frac{\partial}{\partial x} (\frac{x}{x + 3})

Apply the Quotient Rule:

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

= \frac{\frac{\partial}{\partial x} ( x ) ( x + 3 ) - \frac{\partial}{\partial x} ( x + 3 ) x}{( x + 3 ) ^{2}}

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

\frac{\partial}{\partial x} (x + 3) = 1

= \frac{1 \cdot ( x + 3 ) - 1 \cdot x}{( x + 3 ) ^{2}}

1 \cdot (x + 3) - 1 \cdot x = 3

= \frac{3}{( x + 3 ) ^{2}}

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

\frac{d ^{2} y}{d x ^{2}} - 2 \frac{d y}{d x} - 8 y = 0

\int \frac{9}{x - 4} d x

\frac{d}{d x} (tan (4 x^{5}))

\int_{0}^{1} \frac{1}{x - 2} d x

What is (\partial)/(\partial x)(x/(x+3)) ?
The answer to (\partial)/(\partial x)(x/(x+3)) is 3/((x+3)^2)