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

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

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

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

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

Solution steps

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

Treat

y, z

as constants

Apply the Sum/Difference Rule:

(f \pm g)^{'} = f^{'} \pm g^{'}

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

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

\frac{\partial}{\partial x} (3 x z) = 3 z

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

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

\frac{d y}{d x}, 2 x^{2} + y^{2} - 7 = 0

\int \frac{1}{x ^{2} + 2 x + 26} d x

(- 12, 0), (- 15, - 3)

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