What is (\partial)/(\partial x)((2x)/(x^2+y^2+16)) ?

The answer to (\partial)/(\partial x)((2x)/(x^2+y^2+16)) is (2(-x^2+y^2+16))/((x^2+y^2+16)^2)

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(\partial)/(\partial x)((2x)/(x^2+y^2+16))

\frac{\partial}{\partial x} (\frac{2 x}{x ^{2} + y ^{2} + 16})

\frac{2 ( - x ^{2} + y ^{2} + 16 )}{( x ^{2} + y ^{2} + 16 ) ^{2}}

Solution steps

\frac{\partial}{\partial x} (\frac{2 x}{x ^{2} + y ^{2} + 16})

Treat

y

as a constant

Take the constant out:

(a \cdot f)^{'} = a \cdot f^{'}

= 2 \frac{\partial}{\partial x} (\frac{x}{x ^{2} + y ^{2} + 16})

Apply the Quotient Rule:

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

= 2 \cdot \frac{\frac{\partial}{\partial x} ( x ) ( x ^{2} + y ^{2} + 16 ) - \frac{\partial}{\partial x} ( x ^{2} + y ^{2} + 16 ) x}{( x ^{2} + y ^{2} + 16 ) ^{2}}

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

\frac{\partial}{\partial x} (x^{2} + y^{2} + 16) = 2 x

= 2 \cdot \frac{1 \cdot ( x ^{2} + y ^{2} + 16 ) - 2 xx}{( x ^{2} + y ^{2} + 16 ) ^{2}}

Simplify

2 \cdot \frac{1 \cdot ( x ^{2} + y ^{2} + 16 ) - 2 xx}{( x ^{2} + y ^{2} + 16 ) ^{2}} : \frac{2 ( - x ^{2} + y ^{2} + 16 )}{( x ^{2} + y ^{2} + 16 ) ^{2}}

= \frac{2 ( - x ^{2} + y ^{2} + 16 )}{( x ^{2} + y ^{2} + 16 ) ^{2}}

\frac{d}{d x} (\frac{cos ( 2 x )}{x})

3 x^{5} x + \frac{7}{x ^{3} x}

\frac{\partial}{\partial x} (ln (\frac{( x + y )}{x - y}))

\frac{d}{d x} ((4 x + 1)^{2})

\frac{6}{s ^{2} + 5 s + 4}

What is (\partial)/(\partial x)((2x)/(x^2+y^2+16)) ?
The answer to (\partial)/(\partial x)((2x)/(x^2+y^2+16)) is (2(-x^2+y^2+16))/((x^2+y^2+16)^2)