What is the d/(dy)(y/(x^2+y^2+1)) ?

The d/(dy)(y/(x^2+y^2+1)) is (-y^2+x^2+1)/((x^2+y^2+1)^2)

What is the first d/(dy)(y/(x^2+y^2+1)) ?

The first d/(dy)(y/(x^2+y^2+1)) is (-y^2+x^2+1)/((x^2+y^2+1)^2)

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

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

Solution steps

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

Treat

x

as a constant

Apply the Quotient Rule:

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

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

\frac{d y}{d y} = 1

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

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

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

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

\int_{0}^{1} 2 π x (18 - 18 x) d x

\int sin^{2} (x) cos (x) ln (sin (x)) d x

\int sin^{5} (x) \cdot cos^{2} (x) d x

\frac{d}{d x} (x^{3} - 2 x + 1)

\frac{\partial}{\partial x} (2 tan (x y))

What is the d/(dy)(y/(x^2+y^2+1)) ?
The d/(dy)(y/(x^2+y^2+1)) is (-y^2+x^2+1)/((x^2+y^2+1)^2)
What is the first d/(dy)(y/(x^2+y^2+1)) ?
The first d/(dy)(y/(x^2+y^2+1)) is (-y^2+x^2+1)/((x^2+y^2+1)^2)