What is (\partial)/(\partial x)((6x)/(x^2+y^2)) ?

The answer to (\partial)/(\partial x)((6x)/(x^2+y^2)) is (6(-x^2+y^2))/((x^2+y^2)^2)

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(\partial)/(\partial x)((6x)/(x^2+y^2))

\frac{\partial}{\partial x} (\frac{6 x}{x ^{2} + y ^{2}})

\frac{6 ( - x ^{2} + y ^{2} )}{( x ^{2} + y ^{2} ) ^{2}}

Solution steps

\frac{\partial}{\partial x} (\frac{6 x}{x ^{2} + y ^{2}})

Treat

y

as a constant

Take the constant out:

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

= 6 \frac{\partial}{\partial x} (\frac{x}{x ^{2} + y ^{2}})

Apply the Quotient Rule:

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

= 6 \cdot \frac{\frac{\partial}{\partial x} ( x ) ( x ^{2} + y ^{2} ) - \frac{\partial}{\partial x} ( x ^{2} + y ^{2} ) x}{( x ^{2} + y ^{2} ) ^{2}}

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

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

= 6 \cdot \frac{1 \cdot ( x ^{2} + y ^{2} ) - 2 xx}{( x ^{2} + y ^{2} ) ^{2}}

Simplify

6 \cdot \frac{1 \cdot ( x ^{2} + y ^{2} ) - 2 xx}{( x ^{2} + y ^{2} ) ^{2}} : \frac{6 ( - x ^{2} + y ^{2} )}{( x ^{2} + y ^{2} ) ^{2}}

= \frac{6 ( - x ^{2} + y ^{2} )}{( x ^{2} + y ^{2} ) ^{2}}

y^{^{'}} = 2 x + y, y (0) = 7

sin (x) (cos (x) - 1) π

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

x^{2} y^{^{''}} - x y^{^{'}} + y = \frac{1}{x}

\int_{0}^{0.5} 500 x d x

What is (\partial)/(\partial x)((6x)/(x^2+y^2)) ?
The answer to (\partial)/(\partial x)((6x)/(x^2+y^2)) is (6(-x^2+y^2))/((x^2+y^2)^2)