What is (\partial)/(\partial z)(x^2+3yz+4xy) ?

The answer to (\partial)/(\partial z)(x^2+3yz+4xy) is 3y

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(\partial)/(\partial z)(x^2+3yz+4xy)

\frac{\partial}{\partial z} (x^{2} + 3 yz + 4 x y)

3 y

Solution steps

\frac{\partial}{\partial z} (x^{2} + 3 yz + 4 x y)

Treat

x, y

as constants

Apply the Sum/Difference Rule:

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

= \frac{\partial}{\partial z} (x^{2}) + \frac{\partial}{\partial z} (3 yz) + \frac{\partial}{\partial z} (4 x y)

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

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

\frac{\partial}{\partial z} (4 x y) = 0

= 0 + 3 y + 0

Simplify

= 3 y

n = 0 \sum \infty 6 (0.4)^{n}

\frac{d}{d x} (k y (x)^{2})

y^{^{''}} - y = 3 e^{x}

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

n \to \infty lim (\frac{( - 1 ) ^{n + 1}}{2 n - 1})

What is (\partial)/(\partial z)(x^2+3yz+4xy) ?
The answer to (\partial)/(\partial z)(x^2+3yz+4xy) is 3y