What is (\partial)/(\partial y)((z)(x^2+3xy+y^2)) ?

The answer to (\partial)/(\partial y)((z)(x^2+3xy+y^2)) is z(3x+2y)

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(\partial)/(\partial y)((z)(x^2+3xy+y^2))

\frac{\partial}{\partial y} ((z) (x^{2} + 3 x y + y^{2}))

z (3 x + 2 y)

Solution steps

\frac{\partial}{\partial y} ((z) (x^{2} + 3 x y + y^{2}))

Treat

z, x

as constants

Take the constant out:

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

= z \frac{\partial}{\partial y} (x^{2} + 3 x y + y^{2})

Apply the Sum/Difference Rule:

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

= z (\frac{\partial}{\partial y} (x^{2}) + \frac{\partial}{\partial y} (3 x y) + \frac{\partial}{\partial y} (y^{2}))

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

\frac{\partial}{\partial y} (3 x y) = 3 x

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

= z (0 + 3 x + 2 y)

Simplify

= z (3 x + 2 y)

(a e - b d)^{2} + (a f - c d)^{2} + (b f - ce)^{2}

(A + B = 2,) (- 2 A + C = 3)

\frac{5 ( 3 b ^{2} + 4 b - 6 )}{4}

(x - x - 1)^{2}

(x - 13)^{2}

What is (\partial)/(\partial y)((z)(x^2+3xy+y^2)) ?
The answer to (\partial)/(\partial y)((z)(x^2+3xy+y^2)) is z(3x+2y)