What is (\partial)/(\partial x)(x/(sqrt(x+4))) ?

The answer to (\partial)/(\partial x)(x/(sqrt(x+4))) is (x+8)/(2(x+4)sqrt(x+4))

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(\partial)/(\partial x)(x/(sqrt(x+4)))

\frac{\partial}{\partial x} (\frac{x}{x + 4})

\frac{x + 8}{2 ( x + 4 ) x + 4}

Solution steps

\frac{\partial}{\partial x} (\frac{x}{x + 4})

Apply the Quotient Rule:

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

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

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

\frac{\partial}{\partial x} (x + 4) = \frac{1}{2 x + 4}

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

Simplify

\frac{1 \cdot x + 4 - \frac{1}{2 x + 4} x}{( x + 4 ) ^{2}} : \frac{x + 8}{2 ( x + 4 ) x + 4}

= \frac{x + 8}{2 ( x + 4 ) x + 4}

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What is (\partial)/(\partial x)(x/(sqrt(x+4))) ?
The answer to (\partial)/(\partial x)(x/(sqrt(x+4))) is (x+8)/(2(x+4)sqrt(x+4))