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

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

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

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

yz - cos (x + y)

Solution steps

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

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

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

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

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

= yz - 0 - cos (x + y)

Simplify

= yz - cos (x + y)

f (x) = ln (\frac{x - 2}{x + 1})

\int x (7 - y)

\int \frac{1}{9 - 4 x ^{2}} d x

\int_{0}^{\infty} f (a + x) d x

n = 0 \sum \infty \frac{3}{( 1 + i ) ^{n}}

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