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

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

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

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

2 x y

Solution steps

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

Treat

x

as a constant

Take the constant out:

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

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

Apply the Sum/Difference Rule:

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

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

\frac{\partial}{\partial y} (x^{2}) = 0

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

= x (0 + 2 y)

Simplify

= 2 x y

2.6666 (1 + 0.25 = 0)

(e^{3 t} - 1)^{3}

(8.35, - 18.93) x (- 18.93, 7.6) x (2.48, - 8.35)

\frac{( x ^{3} + x ^{2} + 21 )}{x ( 2 x - 5 ) ^{3} ( x ^{2} + 2 x + 5 ) ^{2}}

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