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

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

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

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

2 yz + \frac{3 y}{4}

Solution steps

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

Simplify

2 x yz + \frac{3}{4} x y + z : 2 x yz + \frac{3 x y}{4} + z

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

Treat

y, z

as constants

Apply the Sum/Difference Rule:

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

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

\frac{\partial}{\partial x} (2 x yz) = 2 yz

\frac{\partial}{\partial x} (\frac{3 x y}{4}) = \frac{3 y}{4}

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

= 2 yz + \frac{3 y}{4} + 0

Simplify

= 2 yz + \frac{3 y}{4}

\frac{d y}{d t} + 0.4 t y = 5 t, y (0) = 6

y = x^{3} - 11 x, (2, - 14)

\frac{\partial}{\partial x} (arctan (a) x^{3})

\int \frac{- t}{( t + 1 ) - t + 1} d t

\frac{d z}{d x}

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