What is (\partial)/(\partial x)((-3x)/(x^2+y^2)) ?

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

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(\partial)/(\partial x)((-3x)/(x^2+y^2))

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

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

Solution steps

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

Simplify

\frac{- 3 x}{x ^{2} + y ^{2}} : - \frac{3 x}{x ^{2} + y ^{2}}

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

Treat

y

as a constant

Take the constant out:

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

= - 3 \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}}

= - 3 \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

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

Simplify

- 3 \cdot \frac{1 \cdot ( x ^{2} + y ^{2} ) - 2 xx}{( x ^{2} + y ^{2} ) ^{2}} : - \frac{3 ( - x ^{2} + y ^{2} )}{( x ^{2} + y ^{2} ) ^{2}}

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

\int \frac{1}{x ^{2} + b} d x

\int_{- 8}^{32} \frac{1}{∣ 2 x ∣} d x

\int e^{3} d x

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

\int x^{2} 2 - x^{2} d x

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