What is (\partial)/(\partial x)(z+1-xe^ycos(z)) ?

The answer to (\partial)/(\partial x)(z+1-xe^ycos(z)) is -e^ycos(z)

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(\partial)/(\partial x)(z+1-xe^ycos(z))

\frac{\partial}{\partial x} (z + 1 - x e^{y} cos (z))

- e^{y} cos (z)

Solution steps

\frac{\partial}{\partial x} (z + 1 - x e^{y} cos (z))

Treat

z, y

as constants

Apply the Sum/Difference Rule:

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

= \frac{\partial}{\partial x} (z) + \frac{\partial}{\partial x} (1) - \frac{\partial}{\partial x} (x e^{y} cos (z))

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

\frac{\partial}{\partial x} (1) = 0

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

= 0 + 0 - e^{y} cos (z)

Simplify

= - e^{y} cos (z)

y = (arctan (3 x))^{2}

y^{^{''}} + 9 y^{^{'}} = 5 csc^{2} (3 t)

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

\int (x^{4} (5 - x^{2})) d x

x \to 1000 lim (18 π^{2})

What is (\partial)/(\partial x)(z+1-xe^ycos(z)) ?
The answer to (\partial)/(\partial x)(z+1-xe^ycos(z)) is -e^ycos(z)