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

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

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

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

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

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

Solution steps

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

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

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

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

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

Simplify

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

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

\int x^{2} - 2 x - 8 d x

\int_{3}^{10} (100 - y^{2}) (y + 2) d y

f (x) = x^{3} - 5

\frac{d}{d x} (\frac{1}{x ^{4} + x ^{2} + 1})

\frac{d y}{d x} = \frac{( 2 x ^{4} + 2 y )}{- 2 x - 3 y}

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