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

The answer to (\partial)/(\partial y)(pixsqrt(x^2+y^2)) is (pixy)/(sqrt(x^2+y^2))

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(\partial)/(\partial y)(pixsqrt(x^2+y^2))

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

\frac{π x y}{x ^{2} + y ^{2}}

Solution steps

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

Treat

x

as a constant

Take the constant out:

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

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

Apply the chain rule:

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

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

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

= π x \frac{1}{2 x ^{2} + y ^{2}} \cdot 2 y

Simplify

π x \frac{1}{2 x ^{2} + y ^{2}} \cdot 2 y : \frac{π x y}{x ^{2} + y ^{2}}

= \frac{π x y}{x ^{2} + y ^{2}}

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

\frac{d}{d x} (1 - 3 x)

\frac{d}{d x} (x^{3} + 3 x^{2} - 9 x + 1)

\frac{d}{d x} (e^{8 - x})

\int \frac{1}{x ^{2} + 6 x + 45} d x

What is (\partial)/(\partial y)(pixsqrt(x^2+y^2)) ?
The answer to (\partial)/(\partial y)(pixsqrt(x^2+y^2)) is (pixy)/(sqrt(x^2+y^2))