What is (\partial)/(\partial x)(xyz-sin(x+y+z)) ?

The answer to (\partial)/(\partial x)(xyz-sin(x+y+z)) is yz-cos(x+y+z)

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(\partial)/(\partial x)(xyz-sin(x+y+z))

\frac{\partial}{\partial x} (x yz - sin (x + y + z))

yz - cos (x + y + z)

Solution steps

\frac{\partial}{\partial x} (x yz - sin (x + y + z))

Treat

y, z

as constants

Apply the Sum/Difference Rule:

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

= \frac{\partial}{\partial x} (x yz) - \frac{\partial}{\partial x} (sin (x + y + z))

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

\frac{\partial}{\partial x} (sin (x + y + z)) = cos (x + y + z)

= yz - cos (x + y + z)

\int 8 cot^{4} (x) d x

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

\frac{d}{d x} (4 a sec (x) tan (x))

\int \frac{- x}{1 + x ^{4}} d x

y^{^{'}} + y = 2 e^{x}, y (0) = 20

What is (\partial)/(\partial x)(xyz-sin(x+y+z)) ?
The answer to (\partial)/(\partial x)(xyz-sin(x+y+z)) is yz-cos(x+y+z)