What is (\partial)/(\partial x)(xe^y-yz) ?

The answer to (\partial)/(\partial x)(xe^y-yz) is e^y

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(\partial)/(\partial x)(xe^y-yz)

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

e^{y}

Solution steps

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

Treat

y, z

as constants

Apply the Sum/Difference Rule:

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

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

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

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

= e^{y} - 0

Simplify

= e^{y}

\int_{0}^{\frac{π}{2}} (5 cos^{2} (x)) d x

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

y^{^{''}} - 4 y^{^{'}} + 8 y = 0, y (0) = 9, y (\frac{π}{4}) = 7

x (4.2)

\frac{d}{d x} (tan (x + c))

What is (\partial)/(\partial x)(xe^y-yz) ?
The answer to (\partial)/(\partial x)(xe^y-yz) is e^y