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

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

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

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

x z + sin (x + y + z)

Solution steps

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

Treat

x, z

as constants

Apply the Sum/Difference Rule:

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

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

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

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

= x z - (- sin (x + y + z))

Simplify

= x z + sin (x + y + z)

\frac{d y}{d x} = \frac{4 x + 2 y + 1}{2 x + y + 3}

f (x) = arctan (x)

x - 1

\int_{2}^{4} \frac{1}{5 - 3 x} d x

\int_{6}^{8} \frac{2 x}{x - 5} d x

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