What is (\partial)/(\partial x)(x/(x^2+(y-1)^2)) ?

The answer to (\partial)/(\partial x)(x/(x^2+(y-1)^2)) is (-x^2+(y-1)^2)/((x^2+(y-1)^2)^2)

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(\partial)/(\partial x)(x/(x^2+(y-1)^2))

\frac{\partial}{\partial x} (\frac{x}{x ^{2} + ( y - 1 ) ^{2}})

\frac{- x ^{2} + ( y - 1 ) ^{2}}{( x ^{2} + ( y - 1 ) ^{2} ) ^{2}}

Solution steps

\frac{\partial}{\partial x} (\frac{x}{x ^{2} + ( y - 1 ) ^{2}})

Treat

y

as a constant

Apply the Quotient Rule:

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

= \frac{\frac{\partial}{\partial x} ( x ) ( x ^{2} + ( y - 1 ) ^{2} ) - \frac{\partial}{\partial x} ( x ^{2} + ( y - 1 ) ^{2} ) x}{( x ^{2} + ( y - 1 ) ^{2} ) ^{2}}

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

\frac{\partial}{\partial x} (x^{2} + (y - 1)^{2}) = 2 x

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

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

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

\int \frac{1}{12 x} d x

\frac{d}{d x} (lo g_{5} (x^{2} - 7 x))

v^{'} = - 0.01 v^{2}

y^{^{''}} + 2 y^{^{'}} + 2 y = sin (1 t)

x \to 5 lim (- 2)

What is (\partial)/(\partial x)(x/(x^2+(y-1)^2)) ?
The answer to (\partial)/(\partial x)(x/(x^2+(y-1)^2)) is (-x^2+(y-1)^2)/((x^2+(y-1)^2)^2)