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

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

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

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

2 z

Solution steps

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

Treat

z, x

as constants

Take the constant out:

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

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

Apply the Sum/Difference Rule:

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

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

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

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

\frac{\partial}{\partial y} (3 z) = 0

= z (0 + 2 + 0)

Simplify

= 2 z

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

(c + 4 e^{2} - 3 s^{4})^{2}

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

(x^{2} + 1) e^{3 x}

- \frac{2 ( - 9 x cos ( 9 x ) + sin ( 9 x ) )}{2187}

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