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

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

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

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

2 zy

Solution steps

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

Treat

z, x

as constants

Take the constant out:

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

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

Apply the Sum/Difference Rule:

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

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

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

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

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

= z (0 + 2 y + 0)

Simplify

= 2 zy

x^{\frac{1}{p}} + y (x^{\frac{1}{p}} + 8 y)

\frac{60}{( s + 0.5 + 0.866 j ) ( s + 0.5 - 0.866 j )}

(- 8 π x^{3} + 12) (3)

(6 + i)^{4}

(a + b) l e f t (a^{3} - b^{2})

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