What is (\partial)/(\partial x)(xyzw+2x+3y+4z+w) ?

The answer to (\partial)/(\partial x)(xyzw+2x+3y+4z+w) is yzw+2

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(\partial)/(\partial x)(xyzw+2x+3y+4z+w)

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

yz w + 2

Solution steps

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

Treat

y, z, w

as constants

Apply the Sum/Difference Rule:

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

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

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

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

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

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

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

= yz w + 2 + 0 + 0 + 0

Simplify

= yz w + 2

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

\int (6 x) d x

\frac{\partial}{\partial y} (e^{- y} cos (x))

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

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

What is (\partial)/(\partial x)(xyzw+2x+3y+4z+w) ?
The answer to (\partial)/(\partial x)(xyzw+2x+3y+4z+w) is yzw+2